On Calculations of Zeros of Various L-functions

Hiroyuki Yoshida

On Calculations of Zeros of Various L-functions

Number Theory 2008-02-03 v1

Authors: Hiroyuki Yoshida

Abstract

As we have shown several years ago [Y2], zeros of $L(s, \Delta )$ and $L^(2)(s, \Delta )$ can be calculated quite efficiently by a certain experimental method. Here $\Delta$ denotes the cusp form of weight 12 with respect to SL $(2, Z)$ and $L(s, \Delta )$ (resp. $L^(2)(s, \Delta )$ ) denotes the standard (resp. symmetric square) $L$ -function attached to $\Delta$ . The purpose of this paper is to show that this method can be applied to a wide class of $L$ -functions so that we can obtain precise numerical values of their zeros.

Keywords

L-functions zeros cusp form numerical computation experimental method

Cite

@article{arxiv.math/9411213,
  title  = {On Calculations of Zeros of Various L-functions},
  author = {Hiroyuki Yoshida},
  journal= {arXiv preprint arXiv:math/9411213},
  year   = {2008}
}

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