Bounds of double multiplicative character sums and gaps between residues of exponential functions

Igor E. Shparlinski*, Kam Hung Yau

*Corresponding author for this work

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We derive two new upper bounds on the double multiplicative character sum over subgroups and intervals. Rχ(a,g,I,N)=∑x=1 H|∑n=1 Nχ(x+agn)| where χ is a multiplicative character modulo a prime p, H and N are positive integers and a and g are integers with gcd. (ag, p) = 1. One bound is unconditional and based on a recent result of Cilleruelo and Garaev (2014), the other bound is conditional on the Generalised Riemann Hypothesis (GRH). These bounds complement and improve in some ranges on the recent results of Chang and Shparlinski (2014).

Original languageEnglish
Pages (from-to)304-316
Number of pages13
JournalJournal of Number Theory
Volume167
DOIs
Publication statusPublished - 1 Oct 2016
Externally publishedYes

Keywords

  • Character sums
  • Exponential function
  • Gaps
  • Intervals

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