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A mean-square value of the Riemann zeta function over an arithmetic progression

Number Theory 2023-01-25 v2

Abstract

We obtain an asymptotic formula for the second discrete moment of the Riemann zeta function over the arithmetic progression 12+in\frac{1}{2} + in. It shows that the first main term is equal to that of the continuous mean value.

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Cite

@article{arxiv.2212.06520,
  title  = {A mean-square value of the Riemann zeta function over an arithmetic progression},
  author = {Hirotaka Kobayashi},
  journal= {arXiv preprint arXiv:2212.06520},
  year   = {2023}
}

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10 pages