RAMANUJAN CONGRUENCES FOR A CLASS OF ETA QUOTIENTS-Reference-Cited by-同舟云学术

RAMANUJAN CONGRUENCES FOR A CLASS OF ETA QUOTIENTS

Published:2010-06 Issue:04 Volume:06 Page:835-847
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

SINICK JONAH¹

Affiliation:

1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana IL 61801, USA

Abstract

We consider a class of generating functions analogous to the generating function of the partition function and establish a bound on the primes ℓ for which their coefficients c(n) obey congruences of the form c(ℓn + a) ≡ 0 ( mod ℓ). We apply this result to obtain a complete characterization of the congruences of the same form that the sequences cN(n) satisfy, where cN(n) is defined by [Formula: see text]. This last result answers a question of H.-C. Chan.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042110003253

Reference12 articles.

1. Distribution of the partition function modulo composite integers M

2. Arithmetic properties of the partition function

3. Exceptional congruences for powers of the partition function

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