A generalization of a theorem of Ayoub and Chowla

Redmond, Don

doi:10.1090/S0002-9939-1982-0674083-7

A generalization of a theorem of Ayoub and Chowla
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Proc. Amer. Math. Soc. 86 (1982), 574-580 Request permission

Abstract:

Let $\mathcal {X}1$ and $\mathcal {X}2$ be characters modulo ${q_1}$ and ${q_2}$, respectively, where ${q_1}$ and ${q_2}$ are positive integers. Let \[ f(n) = \sum \limits _{d|n} \mathcal {X}1 (d)\mathcal {X}2(n/d).\] In this paper we shall give an estimate for the sum \[ \sum \limits _{n \leqslant x} {f(n)} \log (x/n). \]

References

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A course in modern analysis