Modular forms with non-vanishing central values and linear independence of Fourier coefficients

Authors

Debargha Banerjee, Indian Institute of Science Education and Research Pune
Priyanka Majumder, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Ramanujan Journal

Abstract

In this article, we are interested in modular forms with non-vanishing central critical values and linear independence of Fourier coefficients of modular forms. The main ingredient is a generalization of a theorem due to VanderKam to modular symbols of higher weights. We prove that for sufficiently large primes p, Hecke operators T1,T2,…,TD act linearly independently on the winding elements inside the space of weight 2k cuspidal modular symbol S2k(Γ0(p)) with k≥1 for D²≪p. This gives a bound on the number of newforms with non-vanishing arithmetic L-functions at their central critical points and linear independence on the reductions of these modular forms for prime modulo l≠p.

First Page

1123

Last Page

1145

DOI

10.1007/s11139-024-00931-5

Publication Date

11-1-2024

Recommended Citation

Banerjee, Debargha and Majumder, Priyanka, "Modular forms with non-vanishing central values and linear independence of Fourier coefficients" (2024). Journal Articles. 4904.
https://digitalcommons.isical.ac.in/journal-articles/4904