Large sieve inequalities with power moduli and Waring's problem
Autor: | Baier, Stephan, Lynch, Sean B. |
---|---|
Rok vydání: | 2023 |
Předmět: | |
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: |