A Bound for a Sum of Products of Two Characters and Its Application

Teerapat Srichan ()
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Teerapat Srichan: Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand

Mathematics, 2023, vol. 11, issue 11, 1-8

Abstract: Using the exponent pair method, a bound is derived for the sum ∑ m a n b ≤ x χ 1 a ( m ) χ 2 b ( n ) , where a , b are fixed positive integers, χ 1 , χ 2 are primitive Dirichlet characters modulo q 1 and q 2 , respectively, and χ 1 a , χ 2 b are not principal characters. As an application, an estimate for the error term in an asymptotic formula for the number of square-full integers simultaneously belonging to two arithmetic progressions is obtained.

Keywords: character sums; Dirichlet convolutions; exponent pair (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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