All modular forms of weight 2 can be expressed by Eisenstein series
Journal article, 2020

We show that every elliptic modular form of integral weight greater thanĀ 1 can be expressed as linear combinations of products of at most two cusp expansions of Eisenstein series. This removes the obstruction of nonvanishing central L -values present in all previous work. For weights greater thanĀ 2, we refine our result further, showing that linear combinations of products of exactly two cusp expansions of Eisenstein series suffice.

Vector-valued Hecke operators

Central values of L -functions

Products of Eisenstein series

Author

Martin Raum

Chalmers, Mathematical Sciences, Algebra and geometry

Jiacheng Xia

Chalmers, Mathematical Sciences, Algebra and geometry

Research in Number Theory

23639555 (eISSN)

Vol. 6 3 32

Real-Analytic Orthogonal Modular Forms as Generating Series

Swedish Research Council (VR), 2020-01-01 -- 2023-12-31.

Siegel modulära genererande funktioner

Swedish Research Council (VR), 2016-01-01 -- 2019-12-31.

Subject Categories

Algebra and Logic

Discrete Mathematics

Mathematical Analysis

DOI

10.1007/s40993-020-00207-z

More information

Latest update

9/1/2020 8