The Generalized Riemann Hypothesis from zeros of a single L-function

William D. Banks

The Generalized Riemann Hypothesis from zeros of a single L-function

Number Theory 2023-09-08 v1

Authors: William D. Banks

Abstract

For each primitive Dirichlet character $\chi$ , a hypothesis ${\rm GRH}^\dagger[\chi]$ is formulated in terms of zeros of the associated $L$ -function $L(s,\chi)$ . It is shown that for any such character, ${\rm GRH}^\dagger[\chi]$ is equivalent to the Generalized Riemann Hypothesis.

Keywords

dirichlet characters generalization theorems

Cite

@article{arxiv.2309.03817,
  title  = {The Generalized Riemann Hypothesis from zeros of a single L-function},
  author = {William D. Banks},
  journal= {arXiv preprint arXiv:2309.03817},
  year   = {2023}
}

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11 pages

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