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Zeros of quasimodular forms and the sum formula for multiple zeta values

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Speaker: 
Jan-Willem van Ittersum
Affiliation: 
Utrecht University/MPI
Date: 
Wed, 2021-10-06 14:30 - 15:30
Parent event: 
Number theory lunch seminar

Zoom ID: 919 6497 4060
For password please contact Pieter Moree (moree@mpim...).

One of the first results every student in modular forms is taught is the valence formula, which gives an expression for the number of zeros of a modular form within each fundamental domain. For extrema or inflection 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 part is based on joint work with Berend Ringeling.
 
Next, we discuss certain algebras of functions on partitions which share many properties with quasimodular forms. As an application, we give a new proof for the sum formula for multiple zeta values. Namely, we show how this formula can be interpreted as a certain limit of polynomial functions in the arm- and leg-lengths of a partition. This part is based on joint work with Henrik Bachmann.
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