Arbeitsgruppe Algebra und Zahlentheorie, MI Köln

Seminare und Vorträge im SS 2024

am Montag, 08. April :

Oberseminar Zahlentheorie

Johann Franke
Title: On the Proportion of Coprime Fractions in Number Fields
Abstract: We determine the asymptotic density of coprime fractions in those of the reduced fractions of number fields. When ordered by norms of denominators, we count a fraction as soon as it "appears" for the first time and no later. The natural density of coprime fractions in the set of reduced fractions may then be computed using well- known facts about Hecke L-functions.

14:00

Übungsraum 2 des Mathematischen Instituts

am Montag, 15. April :

Oberseminar Zahlentheorie

Jan-Willem van Ittersum (1)
Title: Lecture series on q-brackets
Abstract: In this lecture series, we study the generating series of several functions on partitions, that is q-brackets of functions on partitions. In the first lecture, we prove the Bloch-Okounkov theorem, stating that for the class of so-called shifted symmetric functions, such generating series are quasimodular. Then, in the second lecture, we how the study of this subject is being motivated by enumerative geometry. In particular, we study certain functions on partitions naturally associated to representations of symmetric groups, and a second family of functions on partitions related to hook-lengths of partitions. The last lecture will be devoted to results of the speaker, in which q-brackets are related to (generalized) MacMahon series and multiple zeta values.

14:00

Übungsraum 2 des Mathematischen Instituts

am Montag, 22. April :

Oberseminar Zahlentheorie

Jan-Willem van Ittersum (2)
Title: Lecture series on q-brackets
Abstract: See part (1).

14:00

Übungsraum 2 des Mathematischen Instituts

am Montag, 29. April :

Oberseminar Zahlentheorie

Anna Pippich
Title: Sup-norm bounds for Jacobi cusp forms
Abstract: In this talk, we report on new sup-norm bounds for the pointwise Petersson norm for Jacobi forms of integral weight \(k\) and integral index \(m\) for \(\mathrm{SL}_{2}(\mathbb{Z})\), which are normalized with respect to the Petersson inner product. For the proof, we essentially use the representation of the Jacobi cusp forms under consideration as linear combinations of modular forms of weight \(k-\frac{1}{2}\) for some congruence subgroup of \(\mathrm{SL}_{2}(\mathbb{Z})\) (depending on \(m\)) and suitable Jacobi theta functions; we then need to derive bounds for the pointwise Petersson norms of these functions to arrive at our result. This is joint work with A.~Aryasomayajula and J.~Kramer.

14:00

Übungsraum 2 des Mathematischen Instituts