HARMONIC ANALYSIS ON THE POSITIVE RATIONALS I: BASIC RESULTS

J. Math. Sci. Univ. Tokyo
Vol. 23 (2016), No. 3, Page 569–614.

ELLIOTT, PETER D. T. A. ; KISH, JONATHAN
HARMONIC ANALYSIS ON THE POSITIVE RATIONALS I: BASIC RESULTS

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Abstract:
Estimates are given, via harmonic analysis on the positive rationals, for sums of multiplicative functions on progressions whose differences are large in comparison with the length of the sum.

Keywords: Large Sieve, Multiplicative functions, Mean Value, Uniform Distribution, Primes in Arithmetic, Progression.

Mathematics Subject Classification (2010): Primary: 11N37, Secondary: 11F03,11F30,11K65,11L99,11M99,11N64.
Mathematical Reviews Number: MR3526581

Received: 2014-12-09