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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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On the zeros of Dirichlet $L$-functions. I
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by Akio Fujii
Trans. Amer. Math. Soc. 196 (1974), 225-235
DOI: https://doi.org/10.1090/S0002-9947-1974-0349603-2
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Abstract:

A mean value theorem for $\arg L(1/2 + i(t + h), \chi ) - \arg L(1/2 + it, \chi )$ is established. This yields mean estimates for the number of zeros of $L(s, \chi )$ in small boxes.
References
  • A. F. Lavrik, The approximate functional equation for Dirichlet $L$-functions, Trudy Moskov. Mat. Obšč. 18 (1968), 91–104 (Russian). MR 0236126
  • Atle Selberg, Contributions to the theory of the Riemann zeta-function, Arch. Math. Naturvid. 48 (1946), no. 5, 89–155. MR 20594
  • Atle Selberg, Contributions to the theory of Dirichlet’s $L$-functions, Skr. Norske Vid.-Akad. Oslo I 1946 (1946), no. 3, 62. MR 22872
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Bibliographic Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 196 (1974), 225-235
  • MSC: Primary 10H10
  • DOI: https://doi.org/10.1090/S0002-9947-1974-0349603-2
  • MathSciNet review: 0349603