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- W2999687060 abstract "In this paper we obtain a new fully explicit constant for the Pólya–Vinogradov inequality for primitive characters. Given a primitive character $chi$ modulo $q$, we prove the following upper bound: $$ Big| sum_{1 le nle N} chi(n) Big|le c sqrt{q} log q, $$ where $c=3/(4pi^2)+o_q(1)$ for even characters and $c=3/(8pi)+o_q(1)$ for odd characters, with explicit $o_q(1)$ terms. This improves a result of Frolenkov and Soundararajan for large $q$. We proceed, following Hildebrand, to obtain the explicit version of a result by Montgomery–Vaughan on partial Gaussian sums and an explicit Burgess-like result on convoluted Dirichlet characters." @default.
- W2999687060 created "2020-01-23" @default.
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- W2999687060 date "2021-12-13" @default.
- W2999687060 modified "2023-10-16" @default.
- W2999687060 title "Partial Gaussian sums and the Pólya–Vinogradov inequality for primitive characters" @default.
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- W2999687060 doi "https://doi.org/10.4171/rmi/1328" @default.
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