Pólya–Vinogradov and the least quadratic nonresidue

Autor: Leo Goldmakher, Jonathan Bober
Rok vydání: 2015
Předmět:
Zdroj: Bober, J & Goldmakher, L 2016, ' Pólya–Vinogradov and the least quadratic nonresidue ', Mathematische Annalen, vol. 366, no. 1, pp. 853-863 . https://doi.org/10.1007/s00208-015-1353-2
ISSN: 1432-1807
0025-5831
DOI: 10.1007/s00208-015-1353-2
Popis: It is well-known that cancellation in short character sums (e.g. Burgess’ estimates) yields bounds on the least quadratic nonresidue. Scant progress has been made on short character sums since Burgess’ work, so it is desirable to find another approach to nonresidues. In this note we formulate a new line of attack on the least nonresidue via long character sums, an active area of research. Among other results, we demonstrate that improving the constant in the Pólya–Vinogradov inequality would lead to significant progress on nonresidues. Moreover, conditionally on a conjecture on long character sums, we show that the least nonresidue for any odd primitive character (mod k) is bounded by (logk)1.4.
Databáze: OpenAIRE
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