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TRUNCATIONS OF $L$-FUNCTIONS IN RESIDUE CLASSES

Published online by Cambridge University Press:  23 August 2006

IGOR E. SHPARLINSKI
IGOR E. SHPARLINSKI
Affiliation:
Department of Computing, Macquarie University, Sydney, NSW 2109, Australia e-mail: [email protected]
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Abstract

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Let $\chi(n)$ be a quadratic character modulo a prime $p$. For a fixed integer $s\ne 0$, we estimate certain exponential sums with truncated $L$-functions \[L_{s,p}(n) = \sum_{j=1}^n \frac{\chi(\,j)}{j^s}\qquad (n =1, 2, \ldots)\]. Our estimate implies certain uniformly of distribution properties of reductions of $L_{s,p}(n)$ in the residue classes modulo $p$.

Keywords

11L0711M38
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 48 , Issue 2 , May 2006 , pp. 347 - 350
Copyright
2006 Glasgow Mathematical Journal Trust