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On the Product of L(1, χ)

Published online by Cambridge University Press:  22 January 2016

Tikao Tatuzawa
Tikao Tatuzawa*
Affiliation:
Gakushuin University, Tokyo
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Let k(≧3) be a positive integer and φ(k) be the Euler function. We denote by % one of the φ(k) characters formed with modulus k, and by % the principal character. Let Lis, %) be the L-series corresponding to % Throughout the paper we use c and c(ε) to denote respectively an absolute positive constant and a positive constant depending on parameter ε( >0) alone, not necessarily the same at their various occurrences. We use the symbol y = O(Z) for positive X when there exists a c satisfying Y ≦ in the full domain of existence of X and Y.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 5 , February 1953 , pp. 105 - 111
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1953

References

[1] Ankeny, N. C. and Chowla, S.: The class number of the cyclotomic field; Proc. Nat. Acad. Sci. U.S.A, 35 (1949), 529–532.Google Scholar
[2] Brauer, R.: On the zeta-function of algebraic number field II; American Journal of Math. 1950.Google Scholar
[3] Estermann, T.: On Dirichlet’s L-functions; Journal London Math. Soc. 23 (1948), 275–279.Google Scholar
[4] Ingham, A. E.: The distribution of prime numbers; Cambridge, 1932.Google Scholar
[5] Landau, E.: Über Dirichletsche Reihen mit komplexen Charakteren; Crelles Journal Bd. 157.Google Scholar
[6] Landau, E.: Über neuere Fortschritte der additiven Zahlentheorie; Cambridge, 1937.Google Scholar
[7] Page, A.: On the number of the primes in an arithmetic progression; Proc. London Math. Soc. 39 (1935), 116–141.Google Scholar
[8] Tatuzawa, T.: On a theorem of Siegel; Japanese Journal of Math., 1952.Google Scholar