Books

Harmonic Maass forms and mock modular forms: theory and applications
(with A. Folsom, K. Ono, and L. Rolen)
AMS Colloquium Series (2017).
Selected research papers and preprints

The asymptotic distribution of the rank for unimodal sequences
(with C. JenningsShaffer and K. Mahlburg)
submitted for publication.

Some qseries identities extending work of Andrews, Crippa, and Simon on sums of divisors functions
(with C. JenningsShaffer)
submitted for publication.

On a Tauberian theorem of Ingham and EulerMaclaurin summation
(with C. JenningsShaffer and K. Mahlburg)
submitted for publication.

Massive deformations of Maass forms and Jacobi forms
(with M. Berg and T. Gannon)
submitted for publication.

Higher depth quantum modular forms and plumbed 3manifolds
(with K. Mahlburg and A. Milas)
submitted for publication.

Generating functions of planar polygons from homological mirror symmetry of elliptic curves
(with J. Kaszian and J. Zhou)
submitted for publication.

Fourier coefficients of meromorphic modular forms and a question of Petersson
(with B. Kane)
submitted for publication.

An extension of Rohrlich's Theorem to the $j$function
(with B. Kane)
Forum of Mathematics, Sigma, accepted for publication.

Rank two false theta functions and Jacobi forms of negative matrix index
(with J. Kaszian, A. Milas and S. Zwegers)
Advances in Applied Mathematics, accepted for publication.

On the modular completion of certain generating functions
(with S. Ehlen and M. Schwagenscheidt)
International Mathematics Research Notices, accepted for publication.

Quantum modular forms and plumbing graphs of 3manifolds
(with K. Mahlburg and A. Milas)
Journal of Combinatorical Theory, Series A 170 (2020), 105145.

A Note on Andrews’ Partitions with Parts Separated by Parity
(with C. JenningsShaffer)
Annals of Combinatorics 23 (2019), pages 573578.

A framework for modular properties of false theta functions
(with C. Nazaroglu)
Research in the Mathematical Sciences 6:30 (2019), doi:10.1007/s4068701901922.

Unimodal sequence generating functions arising from partition ranks
(with C. JenningsShaffer)
Research in Number Theory 5:25 (2019), doi:10.1007/s409930190164z.

On the rationality of cycle integrals of meromorphic modular forms
(with C. AlfesNeumann and M. Schwagenscheidt)
Mathematische Annalen (2019), doi:10.1007/s00208019019144.

Proofs and reductions of various conjectured partition identities of Kanade and Russell
(with C. JenningsShaffer and K. Mahlburg)
Journal für die reine und angewandte Mathematik (Crelle's Journal) (2019), doi: 10.1515/crelle20190012.

Peak positions of strongly unimodal sequences
(with C. JenningsShaffer, K. Mahlburg and R. Rhoades)
Transactions of the American Mathematical Society 372 (2019), pages 70877109.

An exact formula for $U (3)$ VafaWitten invariants on $\mathbb{P}^2$
(with C. Nazaroglu)
Transactions of the American Mathematical Society 372 (2019), pages 61356159.

Vectorvalued higher depth quantum modular forms and higher Mordell integrals
(with J. Kaszian and A. Milas)
Journal of Mathematical Analysis and Applications 480 (2019), 123397.

On characters of $L_{\frak{sl}_n}(\Lambda_0)$modules
(with K. Mahlburg and A. Milas)
Communications in Contemporary Mathematics (2019), 1950030.

Differential operators on polar harmonic Maass forms and elliptic duality
(with B. Kane and P. Jenkins)
Quarterly Journal of Mathematics 70 (2019), pages 11811207.

Higher depth quantum modular forms, multiple Eichler integrals, and $\mathfrak{sl}_3$ false theta functions
(with J. Kaszian and A. Milas)
Research in the Mathematical Sciences 6:20 (2019), doi:10.1007/s4068701901824.

Regularized inner products of meromorphic modular forms and higher Green's Functions
(with B. Kane and A. von Pippich)
Communications in Contemporary Mathematics 21 (2019), 1850029.

Sums of class numbers and mixed mock modular forms
(with B. Kane)
Mathematical Proceedings of the Cambridge Philosophical Society 7107 (2019), pages 113.

Taylor coefficients of nonholomorphic Jacobi forms and applications
Research in the Mathematical Sciences 5:15 (2018), doi:10.1007/s4068701801326.

Regularized inner products and weakly holomorphic Hecke eigenforms
(with B. Kane)
Journal of Physics A: Mathematical and Theoretical 51 (2018), 044001.

Indefinite theta functions arising in GromovWitten Theory of elliptic orbifolds
(with J. Kaszian and L. Rolen)
Cambridge Journal of Mathematics 6 (2018), pages 2557.

On a modularity conjecture of Andrews, Dixit, Schultz, and Yee for a variation of Ramamunjan's $\omega(q)$
(with C. JenningsShaffer and K. Mahlburg)
Advances in Mathematics 325 (2018), pages 505532.

A classification of harmonic Maass forms
(with S. Kudla)
Mathematische Annalen 370 (2018), pages 17291758.

On Divisors of Modular Forms
(with B. Kane, S. Löbrich, K. Ono, and L. Rolen)
Advances in Mathematics 329 (2018), pages 541554.

On some special families of $q$hypergeometric Maass forms
(with J. Lovejoy and L. Rolen)
International Mathematics Research Notices 2018 (2018), pages 55375561.

Zhu reduction for Jacobi npoint functions and applications
(with M. Krauel and M. Tuite)
Transactions of the American Mathematical Society (2017), doi:10.1090/tran/8013.

The LusztigMacdonaldWall conjectures and $q$difference equations
(with K. Mahlburg and A. Milas)
Contemporary Mathematics 695, Lie Algebras, Vertex Operator Algebras, and Related Topics (2017), pages 41–49.

Asymptotic behavior of partial and false theta functions arising from Jacobi forms and regularized characters
(with A. Folsom and A. Milas)
Journal of Mathematical Physics 58 (2017), 011702.

Improved bounds for Fourier coefficients of Siegel modular forms
Journal of Mathematical Analysis and Applications 451 (2017), pages 11231132.

Regularized inner products and errors of modularity
(with N. Diamantis and S. Ehlen)
International Mathematics Research Notices 2017 (2017), pages 74207458.

$W$algebras, higher rank false theta functions and quantum dimensions
(with A. Milas)
Selecta Mathematica 23 (2017), pages 12491278.

On the AndrewsZagier asymptotics for partitions without sequences
(with B. Kane, D. Parry and R. Rhoades)
Advances in Mathematics 309 (2017), pages 436451.

Kac Wakimoto characters and nonholomorphic Jacobi forms
(with R. Olivetto)
Transaction of the American Mathematical Society 369 (2017), pages 11631184.

Ramanujan and coefficients of meromorphic modular forms
(with B. Kane)
Journal de Mathématiques Pures et Appliquées 107 (2017), pages 100122.

Tropical mirror symmetry for elliptic curves
(with J. Boehm, A. Buchholz, and H. Markwig)
Journal für die Reine und Angewandte Mathematik 732 (2017), pages 211246.

Almost holomorphic Poincare series corresponding to products of harmonic SiegelMaass forms
(with O. Richter and M. WesterholtRaum)
Research in the Mathematical Sciences 3:30 (2016), doi:10.1186/s406870160080y.

Identities for generalized Appell functions and the blowup formula
(with J. Manschot and L. Rolen)
Letters in Mathematical Physics (2016), pages 117.

A problem of Petersson about weight $0$ meromorphic modular forms
(with B. Kane)
Research in the Mathematical Sciences 3:24 (2016), pages 131.

On the Fourier coefficients of negative index meromorphic Jacobi forms
(with L. Rolen and S. Zwegers)
Research in the Mathematical Sciences 3 (2016), pages 19.

On the asymptotic behavior of unimodal rank generating functions
(with B. Kim)
Journal of Mathematical Analysis and Applications 435 (2016), pages 627645.

$p$adic properties of modular shifted convolution Dirichlet series
(with M. Mertens and K. Ono)
Proceedings of the American Mathematical Society 144 (2016), pages 14391451.

Modular local polynomials
(with B. Kane)
Mathematical Research Letters 23 (2016), pages 973987.

On Dyson's crank conjecture and the uniform asymptotic behavior of certain inverse theta functions
(with J. Dousse)
Transaction of the American Mathematical Society 368 (2016), pages 31413155.

A partition identity and the universal mock theta function $g_2(x;q)$
(with J. Lovejoy and K. Mahlburg)
Mathematical Research Letters 23 (2016), pages 6780.

Halfintegral weight padic coupling of weakly holomorphic and holomorphic modular forms
(with P. Guerzhoy and B. Kane)
Research in Number Theory 1:26 (2015), doi:10.1007/s4099301500271.

On the modularity of certain functions from GromovWitten theory of elliptic orbifolds
(with L. Rolen and S. Zwegers)
Royal Society Open Science 2 (2015), doi:10.1098/rsos.150310.

Overpartitions with restricted odd differences
(with J. Dousse, J. Lovejoy, and K. Mahlburg)
Electronic Journal of Combinatorics 22 (2015).

Distinct parts partitions without sequences
(with K. Mahlburg and K. Nataraj)
Electronic Journal of Combinatorics 22 (2015).

On the Fourier expansion of BlochOkounkov npoint function
(with A. Milas)
Journal of Combinatorial Theory A 36 (2015), pages 201219.

MaassJacobi Poincare series and Mathieu moonshine
(with J. Duncan and L. Rolen)
Advances in Mathematics 281 (2015), pages 248278.

Radial limits of mock theta functions
(with L. Rolen)
Research in the Mathematical Sciences 2:17 (2015), doi:10.1186/s4068701500358.

Walgebras, false theta functions, and quantum modular forms, I
(with A. Milas)
International Mathematics Research Notices 21 (2015), pages 1135111387.

Double series representations for Schur's partition function and related identities
(with G. Andrews and K. Mahlburg)
Journal of Combinatorial Theory A 132 (2015), pages 102119.

On cycle integrals of weakly holomorphic modular forms
(with P. Guerzhoy and B. Kane)
Mathematical Proceedings of the Cambridge Philosophical Society 58 (2015), pages 439449.

False theta functions and companions to Caparelli's identities
(with K. Mahlburg)
Advances in Mathematics 278 (2015), pages 121136.

Unimodal sequences and strange functions: a family of quantum modular forms
(with A. Folsom and R. Rhoades)
Pacific Journal of Mathematics 274 (2015), pages 125.

Harmonic MaassJacobi forms with singularities and a thetalike decomposition
(with M. Raum and O. Richter)
Transactions of the American Mathematical Society 367 (2015), pages 66476670.

Locally harmonic Maass forms and the kernel of the Shintani lift
(with B. Kane and W. Kohnen)
International Mathematics Research Notices 1 (2015), pages 31853224.

Negative index Jacobi forms and quantum modular forms
(with T. Creutzig and L. Rolen)
Research in the Mathematical Sciences 1:11 (2014), doi:10.1186/s4068701400118.

Asymptotics for the number of row Fishburn matrices
(with Y. Li and R. Rhoades)
European Journal of Combinatorics 41 (2014), pages 183196.

Asymptotic formulas for stacks and unimodal sequences
(with K. Mahlburg)
Journal of Combinatorial Series A 126 (2014), pages 194215.

Shintani lifts and fractional derivatives of harmonic weak Maass forms
(with P. Guerzhoy and B. Kane)
Advances in Mathematics 255 (2014), pages 641671.

Graded dimensions of principal subspaces and modular AndrewsGordon series
(with C. Calinescu, A. Folsom, and S. Kimport)
Communications on Contemporary mathematics 16 (2014), 1350050.

On a completed generating function of locally harmonic Maass forms
(with B. Kane and S. Zwegers)
Compositio Mathematica 150 (2014), pages 749762.

Asymptotic inequalities for positive crank and rank moments
(with K. Mahlburg)
Transactions of the American Mathematical Society 366 (2014), pages 10731094.

Special $L$values and periods of weakly holomorphic modular forms
(with K. Fricke and Z. Kent)
Proceedings of the American Mathematical Society 142 (2014), pages 34253439.

Almost harmonic Maass forms and KacWakimoto characters
(with A. Folsom)
Journal für die Reine und Angewandte Mathematik 694 (2014), pages 179202.

Taylor coefficients of MockJacobi forms and moments of partition statistics
(with K. Mahlburg and R. Rhoades)
Mathematical Proceedings of the Cambridge Philosophical Society 157 (2014), pages 231251.

Asymptotic formulas for coefficients of inverse theta functions
(with J. Manschot)
Communications in Number Theory and Physics 7 (2013), pages 497513.

On the positivity of black hole degeneracies in string theory
(with S. Murthy)
Communications in Number Theory and Physics 7 (2013), pages 1556.

Theta lifts and local Maass forms
(with B. Kane and M. Viazovska)
Mathematical Research Letters 20 (2013), pages 213234.

$k$run overpartitions and mock theta function
(with A. Holroyd, K. Mahlburg, and M. Vlasenko)
The Quarterly Journal of Mathematics 64 (2013), pages 10091021.

On a conjecture of B. Berndt and B. Kim
(with A. Folsom)
Ramanujan Journal 32 (2013), pages 14.

Mock period functions, sesquiharmonic Maass forms, and noncritical values of $L$functions
(with N. Diamantis and M. Raum)
Advances in Mathematics 233 (2013), pages 115134.

Convolution bootstrap percolation models, Markovtype stochastic processes, and mock theta functions
(with K. Mahlburg and A. Mellit)
International Mathematics Research Notices 2013 (2013), pages 9711013.

Asymptotic formulas for coefficients of KacWakimoto characters
(with K. Mahlburg)
Mathematical Proceedings of the Cambridge Philosophical Society 155 (2013), pages 5172.

On the asymptotic behavior of KacWakimoto characters
(with A. Folsom)
Proceedings of the American Mathematical Society 141 (2013), pages 15671576.

EichlerShimura theory for mock modular forms
(with P. Guerzhoy, Z. Kent, and K. Ono)
Mathematische Annalen 355 (2013), pages 10851121.

From sheaves on $P^2$ to generalizations of the Rademacher expansion
(with J. Manschot)
American Journal of Mathematics 135 (2013), pages 10391065.

Kohnen's limit process for realanalytic Siegel modular forms
(with M. Raum and O. Richter)
Advances in Mathematics 231 (2012), pages 11001118.

Inequalities for full rank differences of $2$marked Durfee symbols
(with B. Kane)
Journal of Combinatorial Theory, Series A 119 (2012), pages 483501.

Mock modular forms as $p$adic modular forms
(with B. Kane and P. Guerzhoy)
Transactions of the American Mathematical Society 364 (2012), pages 23932410.

Improved bounds on metastability thresholds and probabilities for generalized bootstrap percolation
(with K. Mahlburg)
Transactions of the American Mathematical Society 364 (2012), pages 38293859.

Jacobi forms over complex quadratic fields via the cubic Casimir operator
(with C. Conley and O. Richter)
Commentarii Mathematici Helvetici 87 (2012), pages 825859.

$l$adic properties of smallest parts functions
(with S. Ahlgren and J. Lovejoy)
Advances in Mathematics 228 (2011), pages 629645.

Automorphic properties of generating functions for generalized odd rank moments and odd Durfee symbols
(with C. Alfes and J. Lovejoy)
Mathematical Proceedings of the Cambridge Philosophical Society 151 (2011), pages 385406.

Exact formulas for coefficients of Jacobi forms
(with O. Richter)
International Journal of Number Theory 7 (2011), pages 825833.

Asymptotics for rank and crank moments
(with K. Mahlburg and R. Rhoades)
Bulletin of the London Mathematical Society 43 (2011), pages 661672.

Multiplicative $q$hypergeometric series arising from real quadratic fields
(with B. Kane)
Transactions of the American Mathematical Society 363 (2011), pages 21912209.

An extension of the HardyRamanujan Circle Method and applications to partitions without sequences
(with K. Mahlburg)
American Journal of Mathematics 133 (2011), pages 11511178.

Zagiertype dualities and lifting maps for harmonic MaassJacobi forms
(with O. Richter)
Advances in Mathematics 225 (2010), pages 22982315.

Inequalities for differences of Dyson´s rank for all odd moduli
(with B. Kane)
Mathematical Research Letters 17 (2010), pages 927942.

Rankcrank type PDE's and nonholomorphic Jacobi forms
(with S. Zwegers)
Mathematical Research Letters 17 (2010), pages 589600.

Automorphic properties of generating functions for generalized rank moments and Durfee symbols
(with J. Lovejoy and R. Osburn)
International Mathematics Research Notices 2010 (2010), pages 238260.

Dyson's ranks and Maass forms
(with K. Ono)
Annals of Mathematics 171 (2010), pages 419449.

Some characters of Kac and Wakimoto and nonholomorphic modular functions
(with K. Ono)
Mathematische Annalen 345 (2009), pages 547 558.

Inequalities between crank and rank moments
(with K. Mahlburg)
Proceedings of the American Mathematical Society 137 (2009), pages 25672574.

$q$series and weight $3/2$ Maass forms
(with A. Folsom and K. Ono)
Compositio Mathematica 145 (2009), pages 541 552.

Rank and crank moment for overpartitions
(with J. Lovejoy and R. Osburn)
Journal of Number Theory 129 (2009), pages 25672574.

Partition statistics and quasiharmonic Maass forms
(with F. Garvan and K. Mahlburg)
International Mathematics Research Notices 2009 (2009), pages 6397.

Overpartitions and class numbers of binary quadratic forms
(with J. Lovejoy)
Proceedings of the National Academy of Sciences of the United States of America 106 (2009), pages 55135516.

Arithmetic properties of nonharmonic weak Maass forms
(with D. Penniston)
Proceedings of the American Mathematical Society 137 (2009), pages 825833.

On certain congruences for Dyson's ranks
International Journal of Number Theory 5 (2009), pages 573584.

Asymptotics for rank partition functions
Transactions of the Amererican Mathematical Society 361 (2009), pages 34833500.

A Converse Theorem for HilbertJacobi forms
(with S. Hayashida)
The Rocky Mountain Journal of Mathematics 39 (2009), pages 423435.

On the explicit construction of higher deformations of partition statistics
Duke Mathematical Journal 144 (2008), pages 195233.

Eulerian series as modular forms
(with K. Ono and R. Rhoades)
Journal of the American Mathematical Society 21 (2008), pages 10851104.

Rank and congruence for overpartition pairs
(with J. Lovejoy)
International Journal of Number Theory 4 (2008), pages 303322.

Dyson's rank, overpartitions, and weak Maass forms
(with J. Lovejoy)
International Mathematics Research Notices 2007 (2007), doi:10.1093/imrn/rnm063.

Ramanujan type congruences and Jacobi forms
(with B. Heim)
International Mathematics Research Notices 2007 (2007), doi:10.1093/imrn/rnm061.

Lifting elliptic cusp forms to Maass forms with an application to partitions
(with K. Ono)
Proceedings of the National Academy of Sciences of the United States of America 104 (2007), pages 37253731.

On Jacobi Poincare series of small weight
(with T. Yang)
International Mathematics Research Notices 2007 (2007), doi:10.1093/imrn/rnm018.

On a conjecture of Koike on identities between Thompson series and RogerRamanujan function
(with H. Swisher)
Corrigendum
Proceedings of the American Mathematical Society 135 (2007), pages 23172326.

MaassJacobi forms over complex quadratic fields
(with O. Richter and C. Conley)
Mathematical Research Letters 14 (2007), pages 137156.

An arithmetic formula for the partition function
(with K. Ono)
Proceedings of American Mathematical Society 135 (2007), pages 35073514.

Arithmetic properties of coefficients of halfintegral weight MaassPoincaré series
(with K.Ono)
Mathematische Annalen 337 (2007), pages 591612.

The $f(q)$ mock theta function conjecture and partition ranks
(with K. Ono)
Inventiones Mathematicae 165 (2006), pages 243266.

On the boundary behaviour of automorphic forms
(with B. Kane, and W. Kohnen)
International Journal of Number Theory 2 (2006), pages 187194.

Lifting maps from a Vector Space of Jacobi cusp forms to a subspace of elliptic modular forms
Mathematische Zeitschrift 253 (2006), pages 735752.

Estimates of Fourier coefficients of Siegel cusp forms for subgroups and in the case of small weight
Journal of the London Mathematical Society 73 (2006), pages 3147.

Asymptotic Formulas for some restricted partition functions
Ramanujan Journal 12 (2006), pages 257266.

Traces of singular moduli on Hilbert modular surfaces
(with K. Ono and J. Rouse)
International Mathematics Research Notices 47 (2005), pages 28912912.

Identities for traces of singular moduli
(with K. Ono)
Acta Arithmetica 119 (2005), pages 317327.
Conference proceedings and expository papers

Some examples of higher depth vectorvalued quantum modular forms
(with J. Kaszian and A. Milas)
accepted for publication in the proceedings of Ramanujan's 130th birthday conference in Ropar.

Number theoretic generalization of the monster denominator formula
(with B. Kane, S. Löbrich, K. Ono and L. Rolen)
Journal of Physics A: Mathematical and Theoretical 50 (2017), 473001.

Images of MaassPoincaré series in the lower halfplane
(with N. Andersen and L. Rolen)
Contributions in Mathematical and Computational Sciences 10 (2017), pages 923.

Quantum Jacobi forms and finite evaluations of unimodal rank generating functions
(with A. Folsom)
Archiv der Mathematic 107, special volume for E. Gekeler (2016), pages 367378.

Polar harmonic Maass forms and their applications
(with B. Kane)
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 86 (2016), pages 213233.

Halfintegral weight Eichler integrals and quantum modular forms
(with L. Rolen)
Journal of Number Theory 161, special volume in honour of Winnie Li (2016), pages 240254.

Quasimodular forms and sℓ(mm)^ characters
(with A. Folsom and K. Mahlburg)
Corrigendum
Ramanujan Journal 36, special volume in honor of Basil Gordon (2015), pages 103116.

Duality and differential operators for harmonic Maass forms
(with B. Kane and R. Rhoades)
Developments in Mathematics 28, special volume in honour of Ehrenpreis (2013), pages 85106.

Second order cusp forms and mixed mock modular forms
(with B. Kane)
Ramanujan Journal 31, special volume in honour of Ismail and Stanton (2013), pages 147161.

Partial theta functions and mock modular forms as $q$hypergeometric series
(with A. Folsom and R. Rhoades)
Ramanujan Journal 29, special volume for Ramanujan's 125 birthday (2012), pages 295310.

On $q$difference equations for partitions without $k$sequences
(with J. Lovejoy and K. Mahlburg)
The legacy of Ramanujan 20, Ramanujan Mathematical Society (2012), pages 129137.

On the modularity of the inified WRT invariants of certain Seifert manifold
(with K. Hikami and J. Lovejoy)
Advances and Applications in Mathematical Sciences 46, special volume in honour of D. Stanton (2011), pages 8693.

New identities involving sums of tails related to real quadratic fields
(with B. Kane)
Ramanujan Journal 23, special volume in Celebration of Andrews 70th birthday (2010), pages 243251.

Coefficients of harmonic Maass forms
(with K. Ono)
Proceedings of the 2008 University of Florida Conference on Partitions, $q$series, and modular forms (2008).

Mock theta functions, weak Maass forms, and applications
Modular forms, Conference proceedings of the Conference in Schiermonnikoog (2006).

On Fourier coefficients of Siegel cusp forms
Proceedings of the ELAZConference (2004), pages 3443.