Large sieve inequalities with power moduli and Waring's problem

Autor:	Baier, Stephan, Lynch, Sean B.
Rok vydání:	2023
Předmět:	Mathematics - Number Theory 11B57 11P05 (Primary) 11D75 11J71 11L03 11L07 (Secondary)
Zdroj:	Proc. Amer. Math. Soc. 152 (2024), 4593-4605
Druh dokumentu:	Working Paper
DOI:	10.1090/proc/16947
Popis:	We improve the large sieve inequality with $k$th-power moduli, for all $k\ge 4$. Our method relates these inequalities to a restricted variant of Waring's problem. Firstly, we input a classical divisor bound on the number of representations of a positive integer as a sum of two $k$th-powers. Secondly, we input a recent and general result of Wooley on mean values of exponential sums. Lastly, we state a conditional result, based on the conjectural Hardy-Littlewood formula for the number of representations of a large positive integer as a sum of $k+1$ $k$th-powers. Comment: 13 pages, added theorem 2.4 part ii, added corollary 2.6, new comparison section
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2303.07613 Zobrazit plný text záznamu View this record from Arxiv