Non-vanishing theorems for prime twists of some modular $L$-functions

Masataka Chida; Satoshi Wakatsuki

Non-vanishing theorems for prime twists of some modular $L$-functions

Number Theory 2023-10-31 v1

Authors: Masataka Chida , Satoshi Wakatsuki

Abstract

In this paper, we give some non-vanishing results on the central values of prime twists of modular $L$ -functions by imaginary quadratic fields for specific elliptic modular forms. In particular, we show that the central values of prime twists of $L$ -functions of some elliptic modular forms are always non-vanishing whenever the root number is positive.

Keywords

modular L-functions prime twists non-vanishing central values elliptic modular forms imaginary quadratic fields root number

Cite

@article{arxiv.2310.19496,
  title  = {Non-vanishing theorems for prime twists of some modular $L$-functions},
  author = {Masataka Chida and Satoshi Wakatsuki},
  journal= {arXiv preprint arXiv:2310.19496},
  year   = {2023}
}

Comments

20 pages

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