On some weighted average values of l-functions

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Abstract

Let q≥2 and N≥1 be integers. W.Zhang recently proved that for any fixed ε>0 and qε≤N≤q1/2-ε, \[ ∑ χ ≠ χ 0} ∑ Nn=1 χ (n)2 |L(1, χ )|2 = (1 + o(1)) αq q N, where the sum is taken over all nonprincipal characters modulo q, L(1,) denotes the L-functions corresponding to χ, and αq=qo(1) is some explicit function of q. Here we improve this result and show that the same asymptotic formula holds in the essentially full range qNq1.

Original languageEnglish
Pages (from-to)183-186
Number of pages4
JournalBulletin of the Australian Mathematical Society
Volume79
Issue number2
DOIs
Publication statusPublished - Apr 2009

Bibliographical note

Copyright 2009 Cambridge University Press. Article originally published in Bulletin of the Australian Mathematical Society, Vol. 79 No. 2, pp 183-186. The original article can be found at http://dx.doi.org/10.1017/S0004972708001020.

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