Partial Gaussian sums and the Pólya–Vinogradov inequality for primitive characters
Matteo Bordignon
University of New South Wales Canberra, Campbell, Australia
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Abstract
In this paper we obtain a new fully explicit constant for the Pólya–Vinogradov inequality for primitive characters. Given a primitive character modulo , we prove the following upper bound:
where for even characters and for odd characters, with explicit terms. This improves a result of Frolenkov and Soundararajan for large . 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.
Cite this article
Matteo Bordignon, Partial Gaussian sums and the Pólya–Vinogradov inequality for primitive characters. Rev. Mat. Iberoam. 38 (2022), no. 4, pp. 1101–1127
DOI 10.4171/RMI/1328