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SUMS OF MULTIPLICATIVE FUNCTIONS OVER A BEATTY SEQUENCE

Part of: Sequences and sets Forms and linear algebraic groups

Published online by Cambridge University Press:  01 October 2008

AHMET M. GÜLOĞLU  and
C. WESLEY NEVANS
AHMET M. GÜLOĞLU*
Affiliation:
Department of Mathematics, Bilkent University, Bilkent 06800, Ankara, Turkey (email: guloglua@fen.bilkent.edu.tr)
C. WESLEY NEVANS
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211, USA (email: nevans@math.missouri.edu)
*
✉For correspondence; e-mail: guloglua@fen.bilkent.edu.tr
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Abstract

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We study sums involving multiplicative functions that take values over a nonhomogenous Beatty sequence. We then apply our result in a few special cases to obtain asymptotic formulas for quantities such as the number of integers in a Beatty sequence that are representable as a sum of two squares up to a given magnitude.

Keywords

sums of multiplicative functionsBeatty sequences

MSC classification

Secondary: 11E25: Sums of squares and representations by other particular quadratic forms 11B83: Special sequences and polynomials
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 2 , October 2008 , pp. 327 - 334
Copyright
Copyright © 2008 Australian Mathematical Society

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