Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-24T09:34:44.011Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Rights & Permissions [Opens in a new window]

Abstract

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.

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