Books

  1. Harmonic Maass forms and mock modular forms: theory and applications (with A. Folsom, K. Ono, and L. Rolen)
    AMS Colloquium Series, to appear in 2017.

Selected research papers and preprints

  1. Taylor coefficients of non-holomorphic Jacobi forms and applications
    submitted for publication.
  2. Zhu reduction for Jacobi n-point functions and applications (with M. Krauel and M. Tuite)
    submitted for publication.
  3. 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, accepted for publication.
  4. Differential operators on polar harmonic Maass forms and elliptic duality (with B. Kane and P. Jenkins)
    submitted for publication.
  5. Higher depth quantum modulat forms, multiple Eichler integrals, and $\mathfrak{sl}_3$ false theta functions (with J. Kaszian and A. Milas)
    submitted for publication.
  6. Indefinite theta functions arising in Gromov-Witten Theory of elliptic orbifolds (with J. Kaszian and L. Rolen)
    submitted for publication.
  7. On a modularity conjecture of Andrews, Dixit, Schultz, and Yee for a variation of Ramamunjan's $\omega(q)$ (with C. Jennings-Shaffer and K. Mahlburg)
    submitted for publication.
  8. A classification of harmonic Maass forms (with S. Kudla)
    Mathematische Annalen (2017), doi:10.1007/s00208-017-1563-x.
  9. On Divisors of Modular Forms (with B. Kane, S. Löbrich, K. Ono, and L. Rolen)
    submitted for publication.
  10. Regularized inner products of meromorphic modular forms and higher Green's Functions (with B. Kane and A. von Pippich)
    submitted for publication.
  11. Almost holomorphic Poincare series corresponding to products of harmonic Siegel-Maass forms (with O. Richter and M. Westerholt-Raum)
    Research in the Mathematical Sciences, accepted for publication.
  12. 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, accepted for publication.
  13. Improved bounds for Fourier coefficients of Siegel modular forms
    Journal of Mathematical Analysis and Applications, 451, Issue 2 (2017), Pages 1123-1132.
  14. Regularized inner products and errors of modularity (with N. Diamantis and S. Ehlen)
    International Mathematics Research Notices, accepted for publication.
  15. On some special families of $q$-hypergeometric Maass forms (with J. Lovejoy and L. Rolen)
    International Mathematics Research Notices, accepted for publication.
  16. Identities for generalized Appell functions and the blow-up formula (with J. Manschot and L. Rolen)
    Letters in Mathematical Physics, (2016), pages 1-17.
  17. Fourier coefficients of meromorphic modular forms and a question of Petersson (with B. Kane)
    submitted for publication.
  18. Half-integral weight p-adic coupling of weakly holomorphic and holomorphic modular forms (with P.Guerzhoy and B. Kane)
    Research in number theory, (2015), 1: 26.
  19. On the modularity of certain functions from Gromov-Witten theory of elliptic orbifolds (with L. Rolen and S. Zwegers)
    Royal Society Open Science (2015), pages 150310.
  20. $W$-algebras, higher rank false theta functions and quantum dimensions (with A. Milas)
    Selecta Mathematica (2016), doi:10.1007/s00029-016-0289-z.
  21. A problem of Petersson about weight $0$ meromorphic modular forms (with B. Kane)
    Research in the Mathematical Sciences, accepted for publication.
  22. Overpartitions with restricted odd differences (with J. Dousse, J. Lovejoy, and K. Mahlburg)
    Electronic Journal of Combinatorics 3 (2015).
  23. On the Fourier coefficients of negative index meromorphic Jacobi forms (with L. Rolen and S. Zwegers)
    Research in the Mathematical Sciences 3, Issue 1 (2016), pages 1-9.
  24. Distinct parts partitions without sequences (with K. Mahlburg and K. Nataraj)
    Electronic Journal of Combinatorics 22, Issue 3 (2015).
  25. On the Andrews-Zagier asymptotics for partitions without sequences (with B. Kane, D. Parry and R. Rhoades)
    Advances in Mathematics, accepted for publication.
  26. On the asymptotic behavior of unimodal rank generating functions (with B. Kim)
    Journal of Mathematical Analysis and Applications 435, Issue 1 (2016), pages 627-645.
  27. On the Fourier expansion of Bloch-Okounkov n-point function (with A. Milas)
    Journal of Combinatorial Theory A 36 (2015), pages 201-219.
  28. Maass-Jacobi Poincare series and Mathieu moonshine (with J. Duncan and L. Rolen)
    Advances in Mathematics 281 (2015), pages 248-278.
  29. Radial limits of mock theta functions (with L. Rolen)
    Research in the Mathematical Sciences 2 (2015), pages 2-17.
  30. $p$-adic properties of modular shifted convolution Dirichlet series (with M. Mertens and K. Ono)
    Proceedings of the American Mathematical Society, accepted for publication.
  31. Kac Wakimoto characters and non-holomorphic Jacobi forms (with R. Olivetto)
    Transaction of the American Mathematical Society, accepted for publication.
  32. Ramanujan and coefficients of meromorphic modular forms (with B. Kane)
    Journal de Mathématiques Pures et Appliquées, accepted for publication.
  33. W-algebras, false theta functions, and quantum modular forms, I (with A. Milas)
    International Mathematics Research Notices, accepted for publication.
  34. 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 102-119.
  35. On cycle integrals of weakly holomorphic modular forms (with P. Guerzhoy and B. Kane)
    Mathematical Proceedings of the Cambridge Philosophical Society 58 (2015), pages 439-449.
  36. False theta functions and companions to Caparelli's identities (with K. Mahlburg)
    Advances in mathematics 278 (2015), pages 121-136.
  37. Modular local polynomials (with B. Kane)
    Mathematical Research Letters, Vol. 23, No. 4 (2016), pp. 973-987.
  38. Negative index Jacobi forms and quantum modular forms (with T. Creutzig and L. Rolen)
    Research in the Mathematical Sciences 1 (2014), pages 1-32.
  39. 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 3141-3155.
  40. A partition identity and the universal mock theta function $g_2(x;q)$ (with J. Lovejoy and K. Mahlburg)
    Mathematical Research Letters, accepted for publication.
  41. Unimodal sequences and strange functions: a family of quantum modular forms (with A. Folsom and R. Rhoades)
    Pacific Journal of Mathematics 274 (2015), pages 1-25.
  42. Tropical mirror symmetry for elliptic curves (with J. Boehm, A. Buchholz, and H. Markwig)
    Journal für die Reine und Angewandte Mathematik (2015), doi:10.1515/crelle-2014-0143.
  43. Asymptotics for the number of row Fishburn matrices (with Y. Li and R. Rhoades)
    European Journal of Combinatorics 41 (2014), pages 183-196.
  44. Asymptotic formulas for stacks and unimodal sequences (with K. Mahlburg)
    Journal of Combinatorial Series A 126 (2014), pages 194-215.
  45. Asymptotic formulas for coefficients of inverse theta functions (with J. Manschot)
    Communications in Number Theory and Physics 7 (2013), pages 497-513.
  46. Sums of class numbers and mixed mock modular forms (with B. Kane)
    Mathematical Proceedings of the Cambridge Philosophical Society, accepted for publication.
  47. Shintani lifts and fractional derivatives of harmonic weak Maass forms (with P. Guerzhoy and B. Kane)
    Advances in Mathematics 255 (2014), pages 641-671.
  48. Graded dimensions of principal subspaces and modular Andrews-Gordon series (with C. Calinescu, A. Folsom, and S. Kimport)
    Communications on Contemporary mathematics 16 (2014).
  49. On the positivity of black hole degeneracies in string theory (with S. Murthy)
    Communications in number theory and physics 7 (2013), pages 15-56.
  50. Harmonic Maass-Jacobi forms with singularities and a theta-like decomposition (with M. Raum and O. Richter)
    Transactions of the American Mathematical Society 367 (2015), pages 6647-6670.
  51. Theta lifts and local Maass forms (with B. Kane and M. Viazovska)
    Mathematical Research Letters 20 (2013), pages 213-234.
  52. On a completed generating function of locally harmonic Maass forms (with B. Kane and S. Zwegers)
    Compositio Mathematica 150 (2014), pages 749-762.
  53. Asymptotic inequalities for positive crank and rank moments (with K. Mahlburg)
    Transactions of the American Mathematical Society 366 (2014), pages 1073-1094.
  54. 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 3425-3439.
  55. $k$-run overpartitions and mock theta function (with A. Holroyd, K. Mahlburg, and M. Vlasenko)
    The Quarterly Journal of Mathematics 64 (2013), pages 1009-1021.
  56. Almost harmonic Maass forms and Kac-Wakimoto characters (with A. Folsom)
    Journal für die Reine und Angewandte Mathematik 2014 (2014).
  57. Locally harmonic Maass forms and the kernel of the Shintani lift (with B. Kane and W. Kohnen)
    International Mathematics Research Notices 1 (2015), pages 3185-3224.
  58. On a conjecture of B. Berndt and B. Kim (with A. Folsom)
    Ramanujan Journal 32 (2013), pages 1-4.
  59. Mock period functions, sesquiharmonic Maass forms, and non-critical values of $L$-functions (with N. Diamantis and M. Raum)
    Advances in Mathematics 233 (2013), pages 115-134.
  60. Kohnen's limit process for real-analytic Siegel modular forms (with M. Raum and O. Richter)
    Advances in Mathematics 231 (2012), pages 1100-1118.
  61. Convolution bootstrap percolation models, Markov-type stochastic processes, and mock theta functions (with K. Mahlburg and A. Mellit)
    International Mathematics Research Notices 2013 (2013), pages 971-1013.
  62. Asymptotic formulas for coefficients of Kac-Wakimoto characters (with K. Mahlburg)
    Mathematical Proceedings of the Cambridge Philosophical Society 155 (2013), pages 51-72.
  63. Taylor coefficients of Mock-Jacobi forms and moments of partition statistics (with K. Mahlburg and R. Rhoades)
    Mathematical Proceedings of the Cambridge Philosophical Society 157 (2014), pages 231-251.
  64. Inequalities for full rank differences of $2$-marked Durfee symbols (with B. Kane)
    Journal of Combinatorial Theory, Series A 119 (2012), pages 483-501.
  65. $l$-adic properties of smallest parts functions (with S. Ahlgren and J. Lovejoy)
    Advances in Mathematics 228 (2011), pages 629-645.
  66. 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 385-406.
  67. On the asymptotic behavior of Kac-Wakimoto characters (with A. Folsom)
    Proceedings of the American Mathematical Society 141 (2013), pages 1567-1576.
  68. Eichler-Shimura theory for mock modular forms (with P. Guerzhoy, Z. Kent, and K. Ono)
    Mathematische Annalen 355 (2013), pages 1085-1121.
  69. From sheaves on $P^2$ to generalizations of the Rademacher expansion (with J. Manschot)
    American Journal of Mathematics 135 (2013), pages 1039-1065.
  70. Exact formulas for coefficients of Jacobi forms (with O. Richter)
    International Journal of Number Theory 7 (2011), pages 825-833.
  71. Mock modular forms as $p$-adic modular forms (with B. Kane and P. Guerzhoy)
    Transactions of the American Mathematical Society 364 (2012), pages 2393-2410.
  72. Improved bounds on metastability thresholds and probabilities for generalized bootstrap percolation (with K. Mahlburg)
    Transactions of the American Mathematical Society 364 (2012), pages 3829-3859.
  73. Jacobi forms over complex quadratic fields via the cubic Casimir operator (with C. Conley and O. Richter)
    Commentarii Mathematici Helvetici 87 (2012), pages 825-859.
  74. Asymptotics for rank and crank moments (with K. Mahlburg and R. Rhoades)
    Bulletin of the London Mathematical Society 43 (2011), pages 661-672.
  75. Zagier-type dualities and lifting maps for harmonic Maass-Jacobi forms (with O. Richter)
    Advances in Mathematics 225 (2010), pages 2298-2315.
  76. Inequalities for differences of Dyson´s rank for all odd moduli (with B. Kane)
    Mathematical Research Letters 17 (2010), pages 927-942.
  77. Multiplicative $q$-hypergeometric series arising from real quadratic fields (with B. Kane)
    Transactions of the American Mathematical Society 363 (2011), pages 2191-2209.
  78. An extension of the Hardy-Ramanujan Circle Method and applications to partitions without sequences (with K. Mahlburg)
    American Journal of Mathematics 133 (2011), pages 1151-1178.
  79. Some characters of Kac and Wakimoto and nonholomorphic modular functions (with K. Ono)
    Mathematische Annalen 345 (2009), pages 547- 558.
  80. Inequalities between crank and rank moments (with K. Mahlburg)
    Proceedings of the American Mathematical Society 137 (2009), pages 2567-2574.
  81. $q$-series and weight $3/2$ Maass forms (with A. Folsom and K. Ono)
    Compositio Mathematica 145 (2009), pages 541- 552.
  82. Rank-crank type PDE's and non-holomorphic Jacobi forms (with S. Zwegers)
    Mathematical Research Letters 17 (2010), pages 589-600.
  83. Rank and crank moment for overpartitions (with J. Lovejoy and R. Osburn)
    Journal of Number Theory 129 (2009), pages 2567-2574.
  84. 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 238-260.
  85. Partition statistics and quasiharmonic Maass forms (with F. Garvan and K. Mahlburg)
    International Mathematics Research Notices 2009 (2009), pages 63-97.
  86. 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 5513-5516.
  87. On the explicit construction of higher deformations of partition statistics
    Duke Mathematical Journal 144 (2008), pages 195-233.
  88. Eulerian series as modular forms (with K. Ono and R. Rhoades)
    Journal of the American Mathematical Society 21 (2008), pages 1085-1104.
  89. Dyson's rank, overpartitions, and weak Maass forms (with J. Lovejoy)
    International Mathematics Research Notices (2007).
  90. Arithmetic properties of non-harmonic weak Maass forms (with D. Penniston)
    Proceedings of the American Mathematical Society 137 (2009), pages 825-833.
  91. Ramanujan type congruences and Jacobi forms (with B. Heim)
    International Mathematics Research Notices (2007).
  92. Rank and congruence for overpartition pairs (with J. Lovejoy)
    International Journal of Number Theory 4 (2008), pages 303-322.
  93. 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 3725-3731.
  94. On Jacobi Poincare series of small weight (with T. Yang)
    International Mathematics Research Notices (2007).
  95. On a conjecture of Koike on identities between Thompson series and Roger-Ramanujan function (with H. Swisher) Corrigendum
    Proceedings of the American Mathematical Society 135 (2007), pages 2317-2326.
  96. Maass-Jacobi forms over complex quadratic fields (with O. Richter and C. Conley)
    Mathematical Research Letters 14 (2007), pages 137-156.
  97. On certain congruences for Dyson's ranks
    International Journal of Number Theory 5 (2009), pages 573-584.
  98. Asymptotics for rank partition functions
    Transactions of the Amererican Mathematical Society 361 (2009), pages 3483-3500.
  99. Dyson's ranks and Maass forms (with K. Ono)
    Annals of Mathematics 171 (2010), pages 419-449.
  100. The $f(q)$ mock theta function conjecture and partition ranks (with K. Ono)
    Inventiones Mathematicae 165 (2006), pages 243-266.
  101. A Converse Theorem for Hilbert-Jacobi forms (with S. Hayashida)
    The Rocky Mountain Journal of Mathematics 39 (2009), pages 423-435.
  102. On the boundary behaviour of automorphic forms (with B. Kane, and W. Kohnen)
    International Journal of Number Theory 2 (2006), pages 187-194.
  103. An arithmetic formula for the partition function (with K. Ono)
    Proceedings of American Mathematical Society 135 (2007), pages 3507-3514.
  104. Arithmetic properties of coefficients of half-integral weight Maass-Poincaré series (with K.Ono)
    Mathematische Annalen 337 (2007), pages 591-612.
  105. Traces of singular moduli on Hilbert modular surfaces (with K. Ono and J. Rouse)
    International Mathematics Research Notices 47 (2005), pages 2891-2912.
  106. Identities of traces of singular moduli (with K. Ono)
    Acta Arithmetica 119 (2005), pages 317-327.
  107. Lifting maps from a Vector Space of Jacobi cusp forms to a subspace of elliptic modular forms
    Mathematische Zeitschrift 253 (2006), pages 735-752.
  108. 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 31-47.
  109. Asymptotic Formulas for some restricted partition functions
    Ramanujan Journal 12 (2006), pages 257-266.

Conference proceedings

  1. Regularized inner products and weakly holomorphic Hecke eigenforms (with B. Kane)
    submitted for publication.
  2. Images of Maass-Poincaré series in the lower half-plane (with N. Andersen and L. Rolen)
    accepted for publication. Contributions in Mathematical and Computational Sciences.
  3. Quantum Jacobi forms and finite evaluations of unimodal rank generating functions (with A. Folsom)
    accepted for publication. Archiv der Mathematic 107, special volume for E. Gekeler (2016), pages 367-378.
  4. Polar harmonic Maass forms and their applications (with B. Kane)
    Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 86(2), pages 213-233.
  5. Quasimodular forms and sℓ(m|m)^ characters (with A. Folsom and K. Mahlburg) Corrigendum
    Ramanujan Journal 36, special volume in honor of Basil Gordon (2015), pages 103-116.
  6. Half-integral weight Eichler integrals and quantum modular forms (with L. Rolen)
    Ramanujan Journal, special volume in honour of Winnie Li, accepted for publication.
  7. 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 85-106.
  8. 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 147-161.
  9. 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 295-310.
  10. 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 129-137.
  11. 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 86-93.
  12. 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 243-251.
  13. Coefficients of harmonic Maass forms (with K. Ono)
    Proceedings of the 2008 University of Florida Conference on Partitions, $q$-series, and modular forms (2008).
  14. Mock theta functions, weak Maass forms, and applications
    Modular forms, Conference proceedings of the Conference in Schiermonnikoog (2006).
  15. On Fourier coefficients of Siegel cusp forms
    Proceedings of the ELAZ-Conference (2004), pages 34-43.