On the error term in a Parseval type formula in the theory of Ramanujan expansions

JOURNAL OF NUMBER THEORY

卷:156

Article

Murty, M. Ram¹  Saha, Biswajyoti² 

[1] Queens Univ, Dept Math, Kingston, ON K7L 3N6, Canada

[2] Inst Math Sci, Madras 600113, Tamil Nadu, India

关键词: Average order;    Ramanujan expansions;    Parseval type formula;    Error terms;   

DOI  :  10.1016/j.jnt.2015.04.026

来源: Elsevier

【 摘 要 】

Given two arithmetical functions f, g we derive, under suitable conditions, asymptotic formulas with error term, for the convolution sums Sigma(n <= N) f(n)g(n + h), building on an earlier work of Gadiyar, Murty and Padma. A key role in our method is played by the theory of Ramanujan expansions for arithmetical functions. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free