TY - JOUR

T1 - On some weighted average values of l-functions

AU - Shparlinski, Igor E.

N1 - 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.

PY - 2009/4

Y1 - 2009/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77957243717&partnerID=8YFLogxK

U2 - 10.1017/S0004972708001020

DO - 10.1017/S0004972708001020

M3 - Article

AN - SCOPUS:77957243717

VL - 79

SP - 183

EP - 186

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

SN - 0004-9727

IS - 2

ER -