On the critical line zeros of $L$ -- functions attached to automorphic cusp forms

Irina Rezvyakova

On the critical line zeros of $L$ -- functions attached to automorphic cusp forms

Number Theory 2012-12-13 v1

Authors: Irina Rezvyakova

Abstract

We prove for L-function attached to an automorphic cusp form for the Hecke congruence group $\Gamma_0(D)$ , which is also an eigenfunction of all the Hecke operators, that a positive proportion of its non-trivial zeros lie on the critical line. This result extends the work of J.L. Hafner of 1983 where the case of the full modular group is considered.

Keywords

L-functions automorphic cusp forms critical line zeros Hecke congruence group Hecke operators non-trivial zeros modular group

Cite

@article{arxiv.1212.2948,
  title  = {On the critical line zeros of $L$ -- functions attached to automorphic cusp forms},
  author = {Irina Rezvyakova},
  journal= {arXiv preprint arXiv:1212.2948},
  year   = {2012}
}

Comments

20 pages, published in 2010 in Math. Notes

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