We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Online ordering will be unavailable from 17:00 GMT on Friday, April 25 until 17:00 GMT on Sunday, April 27 due to maintenance. We apologise for the inconvenience.
Hostname: page-component-669899f699-cf6xr
Total loading time: 0
Render date: 2025-04-26T12:00:15.715Z
Has data issue: false
hasContentIssue false
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.
[1]Ayoub, R., An introduction to the analytic theory of numbers, Math. Surveys Monographs 10 (Amer. Math. Soc., Providence, 1963).Google Scholar
[2]
[2]Berndt, B. C., ‘Character analogues of the Poisson and Euler-MacLaurin summation formulas with applications’, J. Number Theory7 (1975), 413–445.CrossRefGoogle Scholar
[3]
[3]Berndt, B. C., ‘Classical theorems on quadratic residues’, Enseig. Math. (2) 22 (1976), 261–304.Google Scholar
[4]
[4]Davenport, H., ‘On the series for L(1)’, J. London Math. Soc.24 (1949), 229–233.CrossRefGoogle Scholar
[5]
[5]González-Velasco, E. A., Fourier analysis and boundary value problems (Academic Press, San Diego, 1995).Google Scholar
[6]
[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]
[7]Leu, M.-G., ‘Character sums and the series L(1, χ) with applications to real quadratic fields’, J. Math. Soc. Japan51 (1999), 151–166.CrossRefGoogle Scholar
[8]
[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]
[9]Moser, L., ‘A theorem on quadratic residues’, Proc. Amer. Math. Soc.2 (1951), 503–504.CrossRefGoogle Scholar
[10]
[10]Rademacher, H., Topics in analytic number theory (Springer, New York, 1973).CrossRefGoogle Scholar