Improving the Burgess bound via Pólya-Vinogradov

Improving the Burgess bound via Pólya-Vinogradov

We show that even mild improvements of the Pólya-Vinogradov inequality would imply significant improvements of Burgess’ bound on character sums. Our main ingredients are a lower bound on certain types of character sums (coming from works of the second author jointly with J. Bober and Y. Lamzouri) an...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2019-02, Vol.147 (2), p.461-466
Hauptverfasser: Fromm, Elijah, Goldmakher, Leo
Format: Artikel
Sprache:eng
Schlagworte:
A. ALGEBRA, NUMBER THEORY, AND COMBINATORICS
Research article
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Zusammenfassung:We show that even mild improvements of the Pólya-Vinogradov inequality would imply significant improvements of Burgess’ bound on character sums. Our main ingredients are a lower bound on certain types of character sums (coming from works of the second author jointly with J. Bober and Y. Lamzouri) and a quantitative relationship between the mean and the logarithmic mean of a completely multiplicative function.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/14171