Evaluation of convolution sums Sigma(l+15m=n) sigma(l)sigma(m) and Sigma(3l+5m=n) sigma(l)sigma(m)

Pushpa, K. and Vasuki, K. R. (2022) Evaluation of convolution sums Sigma(l+15m=n) sigma(l)sigma(m) and Sigma(3l+5m=n) sigma(l)sigma(m). Indian Journal of Pure & Applied Mathematics, 53 (4). pp. 1110-1121. ISSN 0975-7465

Text (Full Text) Evaluation of convolution sums.pdf - Published Version Download (319kB)

Abstract

In this article, we have evaluated the convolution sums Sigma(al+bm=n) sigma(l)sigma(m) for a . b = 15, where a, b is an element of N, using an elementary method. The deduced convolution sums are in a little elegent form than that derived by B. Ramakrishnan and B. Sahu 24]. As a consequence, we determine a formula for the number of representations of a positive integer n by the octonary quadratic form (x(1)(2) + x(1)x(2) + x(2)(2) + x(3)(2) + x(3)x(4) + x(4)(2)) + 5 (x(5)(2) + x(5)x(6) + x(6)(2) + x(7)(2) + x(7)x(8) + x(8)(2)).

Item Type:	Article
Uncontrolled Keywords:	Dedekind eta function; Ramanujan's theta function; Eisenstein series; Divisors function
Subjects:	E Mathematical Science > Mathematics
Divisions:	Department of > Mathematics
Depositing User:	C Swapna Library Assistant
Date Deposited:	12 Jul 2023 10:53
Last Modified:	12 Jul 2023 10:53
URI:	http://eprints.uni-mysore.ac.in/id/eprint/17611

Actions (login required)

View Item