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Theta Cycles of Modular Forms Modulo
Scott Ahlgren, Martin Raum, Olav K. Richter
The theta cycle of a modular form modulo a prime is well understood. By contrast, the theta cycle modulo a power of is still mysterious and experimentally erratic. He…
Jacobi Forms of Affine Weight in Higher Cogenus and Nearly Holomorphic Functions
Jan Feldmann, Martin Raum
We describe Jacobi forms of vector-valued weights in terms of classical ones, extending previous results by Ibukiyama and Kyomura to the case of arbitrary cogenus. As in their resu…
Correction to "Kudla's Modularity Conjecture and Formal Fourier-Jacobi Series"
Jan Hendrik Bruinier, Martin Raum
We correct an error in Lemma 4.4 and its application in Theorem 4.5 in our paper ``Kudla's Modularity Conjecture and Formal Fourier-Jacobi Series''.
Eisenstein series modulo
Scott Ahlgren, Michael Hanson, Martin Raum +1
We study congruences for Eisenstein series on modulo , where is prime. It is classically known that all Eisenstein series of weight at l…
The Bernstein-Gelfand Tensor Product Functor and the Weight-2 Eisenstein Series
Martin Raum
The Bernstein-Gelfand tensor product functors are endofunctors of the category of Harish-Chandra modules provided by tensor products with finite dimensional modules. We provide an…
Eichler integrals and generalized second order Eisenstein series
Albin Ahlbäck, Tobias Magnusson, Martin Raum
We show that all Eichler integrals, and more generally all "generalized second order modular forms" can be expressed as linear combinations of corresponding generalized second orde…