Boundedness of denominators of special values of the L-functions for modular forms

Hidenori Katsurada

Boundedness of denominators of special values of the L-functions for modular forms

Number Theory 2022-04-08 v3

Authors: Hidenori Katsurada

Abstract

For a cuspidal Hecke eigenform $F$ for $Sp_n(Z)$ and a Dirichlet character $\chi$ let $L(s,F,\chi,St)$ be the standard $L$ -function of $F$ twisted by $\chi$ . Boecherer showed the boundedness of denominators of the algebraic part of $L(m,F,\chi,St)$ at a critical point $m$ when $\chi$ varies. In this paper, we give a refined version of his result We also prove a similar result for the products of Hecke $L$ functions of primitive forms for $SL_2(Z)$ .

Keywords

modular forms l-functions denominators hecke eigenforms dirichlet characters

Cite

@article{arxiv.2106.10873,
  title  = {Boundedness of denominators of special values of the L-functions for modular forms},
  author = {Hidenori Katsurada},
  journal= {arXiv preprint arXiv:2106.10873},
  year   = {2022}
}

Boundedness of denominators of special values of the L-functions for modular forms

Abstract

Keywords

Cite

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