Seminare und Vorträge im SS 2026

am Montag, 27. April :

Oberseminar Zahlentheorie

Debmalya Basak
Title: Surfaces Associated to Zeros of Automorphic L-functions
Abstract: Assuming the Riemann Hypothesis, Montgomery established results concerning pair correlation of zeros of the Riemann zeta function. Rudnick and Sarnak extended these results to automorphic L-functions and all level correlations. We show that automorphic L-functions exhibit additional geometric structures related to the correlation of their zeros. This is joint work with Cruz Castillo and Alexandru Zaharescu.

14:00 Übungsraum 2 des Mathematischen Instituts

am Montag, 11. Mai :

Oberseminar Zahlentheorie

Matthias Storzer
Title: Knots, q-series, and modular forms
Abstract: To study knots, invariants like the colored Jones polynomials (CJP) are used. For alternating knots, it is known that the coefficients of the CJP stabilize and thus, they converge to a well-defined q-series, the tail of the CJP. For several but not all knots with up to 10 crossings, the tail of the CJP can be written as a product of (partial) theta functions and thus has modular properties. In this talk, we present a general formula for a class of knots, and argue that the tail of the CJP for other knots does not have any modular properties. We will also discuss a potential connection to exceptional hyperbolic surgery on knots. This talk is based on joint work with Robert Osburn (Cork).

14:00 Übungsraum 2 des Mathematischen Instituts

am Montag, 01. Juni :

Oberseminar Zahlentheorie

Rajat Gupta
Title: Koshliakov zeta functions and summation formulas
Abstract: In this talk I will revisit the theory of Koshliakov zeta functions, which was unstudied for more than 70 years of its appearance in his manuscript in 1949. Using this theory, I will present a unified framework which unify some of the summation formulas given by Ramanujan. If time permits, I will also present the extension of Ramanujan's formula for odd zeta values via Koshliakov's theory and ongoing work in this theory. This is a joint work with Professor Bruce C. Berndt and Professor Atul Dixit, soon appearing in Subbarao's volume.

14:00 Übungsraum 2 des Mathematischen Instituts

am Montag, 15. Juni :

Oberseminar Zahlentheorie

Sanoli Gun
Title: On moments of L-functions
Abstract: Moments of Riemann zeta function have been studied extensively in analytic number theory. Some of these results have been extended to other classes of L-functions. In this talk, we will report on some recent work concerning moments of a large class of L-functions. This is a joint work with Gaurav Kumar and Deep Thakur.

14:00 Übungsraum 2 des Mathematischen Instituts

am Montag, 22. Juni :

Oberseminar Zahlentheorie

Chan Heng Huat
Title: On Schutlz's generalization of the Borweins identity
Abstract: In this talk, we revisit Schultz's extension of the Borweins identity. This talk is based on joint work with Song Heng Chan, ZhiGuo Liu and Wadim Zudilin.

14:00 Übungsraum 2 des Mathematischen Instituts

am Montag, 13. Juli :

Oberseminar Zahlentheorie

Pavel Guerzhoy
Title: Congruences for traces of singular moduli and Hurwitz-Kronecker class numbers
Abstract: Traces of singular moduli were introduced by Zagier in 1988. These integers have deep interpretation and lots of interesting properties, congruences in particular. An amount of research triggered by observations and questions of Ken Ono was devoted to these congruences. We present an alternative approach which allows us to consider the congruences as congruences between weight 3/2 modular forms under repeated action of Atkin's U-operator. Besides a general result which includes previously known results as special cases, our approach allows for a quantification of some qualitative results obtained earlier using different methods. As another amusing application, we obtain a modulo 11 congruence parallel to (but conceptually different from) a famous modulo 5 congruence demonstrated by Mazur in 1979.

14:00 Übungsraum 2 des Mathematischen Instituts

am Montag, 20. Juli :

Oberseminar Zahlentheorie

Glenn Bruda
Title:
Abstract:

14:00 Übungsraum 2 des Mathematischen Instituts

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