Glasgow Mathematical Journal

Table of Contents - 2006 - Volume 48, Issue 02  


TRUNCATIONS OF $L$-FUNCTIONS IN RESIDUE CLASSES

IGOR E. SHPARLINSKI a1 1
a1 Department of Computing, Macquarie University, Sydney, NSW 2109, Australia e-mail: igor@ics.mq.edu.au

Article author query
shparlinski ie   [Google Scholar] 
 

Abstract

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 $p$.

(Published Online August 23 2006)
(Received December 9 2005)
(Accepted February 10 2006)

Maths Classification

11L07; 11M38.

Footnotes

1 During the preparation of this paper, the author was supported in part by ARC grant DP0556431.