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False and partial Eisenstein series related to unimodal sequences
Kathrin Bringmann, Badri Vishal Pandey, Jan-Willem van Ittersum
Motivated by the fact that the classical Jacobi theta function is the exponential generating function of the Eisenstein series, we study the exponential Taylor coeffici…
Integer partitions detect the primes
William Craig, Jan-Willem van Ittersum, Ken Ono
We show that integer partitions, the fundamental building blocks in additive number theory, detect prime numbers in an unexpected way. Answering a question of Schneider, we show th…
Limiting behaviour and modular completions of MacMahon-like q-series
Kathrin Bringmann, William Craig, Jan-Willem van Ittersum +1
Recently, MacMahon's generalized sum-of-divisor functions were shown to link partitions, quasimodular forms, and q-multiple zeta values. In this paper, we explore many further prop…
On the zeros of odd weight Eisenstein series
Jan-Willem van Ittersum, Berend Ringeling
We count the number of zeros of the holomorphic odd weight Eisenstein series in all -translates of the standard fundamental domain.
Formal multiple Eisenstein series and their derivations
Henrik Bachmann, Jan-Willem van Ittersum, Nils Matthes
We introduce the algebra of formal multiple Eisenstein series and study its derivations. This algebra is motivated by the classical multiple Eisenstein series, introduced by Gangl-…