Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-22T13:51:30.020Z Has data issue: false hasContentIssue false
  • English
  • Français

Character sums and the series L(1, χ)

Part of: Zeta and $L$-functions: analytic theory Exponential sums and character sums Algebraic number theory: global fields Sequences and sets

Published online by Cambridge University Press:  09 April 2009

Ming-Guang Leu
Ming-Guang Leu
Affiliation:
Department of Mathematics National Central UniversityChung-Li, Taiwan 32054Republic of China e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we derive a relation between character sums and partial sums of Dirichlet series.

Keywords

character sumsDirichlet series

MSC classification

Secondary: 11M20: Real zeros of $L(s, chi)$; results on $L(1, chi)$ 11L99: None of the above, but in this section 11R11: Quadratic extensions 11R29: Class numbers, class groups, discriminants 11B68: Bernoulli and Euler numbers and polynomials
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 70 , Issue 3 , June 2001 , pp. 425 - 436
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Ayoub, R., An introduction to the analytic theory of numbers, Math. Surveys Monographs 10 (Amer. Math. Soc., Providence, 1963).Google Scholar
[2]Berndt, B. C., ‘Character analogues of the Poisson and Euler-MacLaurin summation formulas with applications’, J. Number Theory 7 (1975), 413–445.CrossRefGoogle Scholar
[3]Berndt, B. C., ‘Classical theorems on quadratic residues’, Enseig. Math. (2) 22 (1976), 261–304.Google Scholar
[4]Davenport, H., ‘On the series for L(1)’, J. London Math. Soc. 24 (1949), 229–233.CrossRefGoogle Scholar
[5]González-Velasco, E. A., Fourier analysis and boundary value problems (Academic Press, San Diego, 1995).Google Scholar
[6]Leu, M.-G., ‘On L(1, χ) and class number formula for the real quadratic fields’, Proc. Japan Acad. 72A (1996), 69–74.Google Scholar
[7]Leu, M.-G., ‘Character sums and the series L(1, χ) with applications to real quadratic fields’, J. Math. Soc. Japan 51 (1999), 151–166.CrossRefGoogle Scholar
[8]Leu, M.-G. and Li, W.-C. Winnie, ‘On the series for L(1, χ)’, Nagoya Math. J. 141 (1996), 125–141.CrossRefGoogle Scholar
[9]Moser, L., ‘A theorem on quadratic residues’, Proc. Amer. Math. Soc. 2 (1951), 503–504.CrossRefGoogle Scholar
[10]Rademacher, H., Topics in analytic number theory (Springer, New York, 1973).CrossRefGoogle Scholar