A Generalization of A Theorem of Ayoub and Chowla

Let $\chi_1$ and $\chi_2$ be characters modulo $q_1$ and $q_2$, respectively, where $q_1$ and $q_2$ are positive integers. Let $$f(n) = \sum_{d\mid n} \chi_1(d)\chi_2(n/d).$$ In this paper we shall give an estimate for the sum $$\sum_{n \leq x} f(n)\log(x/n).$$

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1982-12, Vol.86 (4), p.574-580
Main Author: Redmond, Don
Format: Article
Language:English
Subjects:
Mathematical theorems
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Summary:Let $\chi_1$ and $\chi_2$ be characters modulo $q_1$ and $q_2$, respectively, where $q_1$ and $q_2$ are positive integers. Let $$f(n) = \sum_{d\mid n} \chi_1(d)\chi_2(n/d).$$ In this paper we shall give an estimate for the sum $$\sum_{n \leq x} f(n)\log(x/n).$$
ISSN:0002-9939
1088-6826
DOI:10.1090/s0002-9939-1982-0674083-7