On partial sums of arithmetical functions of two variables with absolutely convergent Ramanujan expansions View Full Text


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Article Info

DATE

2018-12-17

AUTHORS

Ritika Sharma

ABSTRACT

In this article, we derive an asymptotic formula for the sums of the form ∑n1,n2≤Nf(n1,n2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sum }_{n_{1},n_{2}\le N}f(n_1,n_2)$$\end{document} with an explicit error term, for any arithmetical function f of two variables with absolutely convergent Ramanujan expansion and Ramanujan coefficients satisfying certain hypothesis.

PAGES

3

References to SciGraph publications

  • 2014-10. Ramanujan — Fourier series and a theorem of Ingham in INDIAN JOURNAL OF PURE AND APPLIED MATHEMATICS
  • 1980-12. Ramanujan expansions of bounded arithmetic functions in ARCHIV DER MATHEMATIK
  • 2015-04-30. On generalized Ramanujan primes in THE RAMANUJAN JOURNAL
  • 1970-12. The number of pairs of integers with L. C. M. ≦ x in ARCHIV DER MATHEMATIK
  • 2016-07-15. Partial sums of arithmetical functions with absolutely convergent Ramanujan expansions in PROCEEDINGS - MATHEMATICAL SCIENCES
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    http://scigraph.springernature.com/pub.10.1007/s12044-018-0446-8

    DOI

    http://dx.doi.org/10.1007/s12044-018-0446-8

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