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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the zeros of Dirichlet $ L$-functions. I


Author: Akio Fujii
Journal: Trans. Amer. Math. Soc. 196 (1974), 225-235
MSC: Primary 10H10
MathSciNet review: 0349603
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Abstract: A mean value theorem for $ \arg \;L({\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.... ...e 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}} + it,\chi )$ is established. This yields mean estimates for the number of zeros of $ L(s,\chi )$ in small boxes.


References [Enhancements On Off] (What's this?)

  • [1] A. F. Lavrik, An approximate functional equation for Dirichlet L-functions, Trudy Moskov. Mat. Obšč. 18 (1968), 91-104 = Trans. Moscow Math. Soc. 18 (1968), 101-116. MR 38 #4424. MR 0236126 (38:4424)
  • [2] A. Selberg, Contributions to the theory of the Riemann zeta-function, Arch. Math. Naturvid. 48 (1946), no. 5, 89-155. MR 8, 567. MR 0020594 (8:567e)
  • [3] -, Contributions to the theory of Dirichlet's L-functions, Skr. Norske Vid-Akad. Oslo I 1946, no. 3, 2-62. MR 9, 271. MR 0022872 (9:271i)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0349603-2
PII: S 0002-9947(1974)0349603-2
Keywords: Riemann zeta function, Dirichlet L-functions, distribution of zeros
Article copyright: © Copyright 1974 American Mathematical Society