A refinement of the Burgess bound for character sums

2017/11/28 by Kerr, Bryce, Shparlinski, Igor E., Yau, Kam Hung
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1711.10582

Abstract

In this paper we give a refinement of the bound of D. A. Burgess for multiplicative character sums modulo a prime number q. This continues a series of previous logarithmic improvements, which are mostly due to H. Iwaniec and E. Kowalski. In particular, for any nontrivial multiplicative character χ modulo a prime q and any integer r≥ 2, we show that ∑_M

Related

• Character Sums Over The Prime Numbers
• Burgess's Bounds for Character Sums
• Burgess bounds for short character sums evaluated at forms II: the mixed case
• Explicit Burgess Bound for Composite Moduli
• Improving the Burgess bound via Polya-Vinogradov