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ON THE MEAN VALUES OF L(1, χ)

Wenpeng Zhang|Zhaoxia Wu
대한수학회 (The Korean Mathematical Society)|2012.12|대한수학회보 (Bulletin of the KMS)|제49권 제6호|pp. 1303-1310

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참고문헌

키워드

identityDirichlet characterL-function
주제분류수학

초록

Let $p$ > 2 be a prime, and let $k{\geq}1$ be an integer. Let χ be a Dirichlet character modulo $p$, and let $L(s,{\chi})$ be the Dirichlet L-function corresponding to χ. In this paper we consider the mean values of $$\sum_{{\chi}\;mod\;p\\{\chi}(-1)=-1}{\chi}(2^k)|L(1,\chi)|^2$$.

Abstract

Let $p$ > 2 be a prime, and let $k{\geq}1$ be an integer. Let χ be a Dirichlet character modulo $p$, and let $L(s,{\chi})$ be the Dirichlet L-function corresponding to χ. In this paper we consider the mean values of $$\sum_{{\chi}\;mod\;p\\{\chi}(-1)=-1}{\chi}(2^k)|L(1,\chi)|^2$$.

참고문헌 (8)

  1. T. M. Apostol, "Introduction to Analytic Number Theory" (1976), Springer-Verlag
  2. T. Funakura, "On Kronecker’s limit formula or Dirichlet series with periodic coefficients", Acta Arith, 55(1), pp.59~73 (1990)
  3. M. Katsurada, "The mean value of Dirichlet L-functions at integer points and class numbers of cyclotomic fields", Nagoya Math. J, 134, pp.151~172 (1994)
  4. H. Liu, "On the mean value of at positive integers m", Acta Arith, 122(1), pp.51~56 (2006)
  5. S. Louboutin, "Quelques formules exactes pour des moyennes de fonctions L de Dirichlet", Canad. Math. Bull, 36(2), pp.190~196 (1993)
  6. S. Louboutin, "On the mean value of for odd primitive Dirichlet characters", Proc. Japan Acad. Ser. A Math. Sci, 75(7), pp.143~145 (1999)
  7. S. Louboutin, "The mean value of at positive rational integers", Colloq. Math, 90(1), pp.69~76 (2001)
  8. H. Walum, "An exact formula for an average of L-series", Illinois J. Math, 26(1), pp.1~3 (1982)

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