Average sizes of mixed character sums Wang, Victor ; https://orcid.org/0000-0002-0704-7026 Xu, Max ddc:510 We prove that the average size of a mixed character sum (math. formular) (for a suitable smooth function w) is on the order of √x for all irrational real θ satisfying a weak Diophantine condition, where χ is drawn from the family of Dirichlet characters modulo a large prime r and where x 6 r. In contrast, it was proved by Harper that the average size is o(√x) for rational θ. Certain quadratic Diophantine equations play a key role in the present paper. Cambridge University Press 2026 info:eu-repo/semantics/article doc-type:article article http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/21385 Wang V, Xu M. Average sizes of mixed character sums. <i>Proceedings of the Royal Society of Edinburgh: Section A Mathematics</i>. 2026:1-15. doi:<a href="https://doi.org/10.1017/prm.2026.10123">10.1017/prm.2026.10123</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1017/prm.2026.10123 info:eu-repo/semantics/altIdentifier/issn/0308-2105 info:eu-repo/semantics/altIdentifier/e-issn/1473-7124 info:eu-repo/semantics/altIdentifier/arxiv/2411.14181 info:eu-repo/semantics/openAccess