Number theory seminar

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Date / Time

Speaker

Title

Location

5 November 2021
14:15-15:15

Dr. Danylo Radchenko
ETH Zurich, Switzerland

Event Details

Title	Arithmetic properties of the Herglotz function
Speaker, Affiliation	Dr. Danylo Radchenko, ETH Zurich, Switzerland
Date, Time	5 November 2021, 14:15-15:15
Location	HG G 43
Abstract	I will talk about a special function, first considered by Herglotz, that has some interesting connections to number theory. Among these are its appearance in the Kronecker limit formula for real quadratic fields, functional equations coming from Hecke operators, and a connection between its special values in quadratic fields and Stark's conjectures. The talk is based on a recent joint work with Don Zagier.

Arithmetic properties of the Herglotz functionread_more

12 November 2021
14:15-15:15

Dr. Jan-Willem van Ittersum
MPI Bonn

Event Details

Title	Critical points of modular forms
Speaker, Affiliation	Dr. Jan-Willem van Ittersum, MPI Bonn
Date, Time	12 November 2021, 14:15-15:15
Location	HG G 43
Abstract	By the valence formula the number of zeros of a modular form within each fundamental domain is known. For critical points of modular forms much less is known. We discuss recent results on the zeros of derivatives of modular forms, or, more generally, on the zeros of quasimodular forms. This is based on joint work with Berend Ringeling.

Critical points of modular formsread_more

19 November 2021
14:15-15:15

Dr. Markus Schwagenscheidt
ETH Zurich, Switzerland

Event Details

Title	Fourier coefficients of harmonic Maass forms
Speaker, Affiliation	Dr. Markus Schwagenscheidt, ETH Zurich, Switzerland
Date, Time	19 November 2021, 14:15-15:15
Location	HG G 43
Abstract	The theory of harmonic Maass forms, which are non-holomorphic generalizations of classical elliptic modular forms, was developed around 2000 by Bruinier and Funke and has since then become a vital area of research, with applications to understanding mock modular forms, derivatives of L-functions of newforms, and special values of automorphic Green functions, among others. An important problem is to understand the algebraic proberties of Fourier coefficients of harmonic Maass forms. In this talk we give an overview on results in this direction. In particular, we show that there are infinite families of harmonic Maass forms related to unary and binary theta functions which indeed have algebraic Fourier coefficients.

Fourier coefficients of harmonic Maass formsread_more

3 December 2021
14:15-15:15

Dr. Paloma Bengoechea Duro
ETH Zurich, Switzerland

Event Details

Title	Distribution of cycle integrals of modular functions and continued fractions
Speaker, Affiliation	Dr. Paloma Bengoechea Duro, ETH Zurich, Switzerland
Date, Time	3 December 2021, 14:15-15:15
Location	HG G 43
Abstract	Cycle integrals of a modular function are integrals along hyperbolic geodesics which endpoints are the two roots of an indefinite binary quadratic form with integer coefficients. Cycle integrals of Klein's $j$ modular function have recently gained importance partly because of their similarities with singular moduli discovered by Duke-Imamoglu-Toth. I will discuss new results on the values and distribution of cycle integrals that rely on diophantine approximation.

Distribution of cycle integrals of modular functions and continued fractionsread_more

17 December 2021
14:15-15:15

Dr. Steven Charlton
Universität Hamburg

Event Details

Title	Generators of multiple t values, and alternating multiple zeta values
Speaker, Affiliation	Dr. Steven Charlton, Universität Hamburg
Date, Time	17 December 2021, 14:15-15:15
Location	HG G 43
Abstract	Multiple zeta values, and their relatives including the multiple t values, are a prominent but mysterious class of real numbers, which appear in various areas from high energy physics and knot theory, to number theory and the periods of mixed Tate motives. I will review some work by Francis Brown, and some recent work by Takuya Murakami, on how to prove certain elements \zeta(2's and 3's), and t(2's and 3's), generate the space of multiple zeta values. I will then extend Murakami's work to show t(1's and 2's) generate the space of multiple t values and alternating multiple zeta values, and make some progress towards Saha's conjecture that t(1's and 2's, 2 or 3) are a basis for convergent MtV’s.

Generators of multiple t values, and alternating multiple zeta valuesread_more

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