RAMANUJAN'S CUBIC CONTINUED FRACTION AND RAMANUJAN TYPE CONGRUENCES FOR A CERTAIN PARTITION FUNCTION-Reference-Cited by-同舟云学术

RAMANUJAN'S CUBIC CONTINUED FRACTION AND RAMANUJAN TYPE CONGRUENCES FOR A CERTAIN PARTITION FUNCTION

Published:2010-06 Issue:04 Volume:06 Page:819-834
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

CHAN HEI-CHI¹

Affiliation:

1. University of Illinois at Springfield, Springfield, IL 62703-5407, USA

Abstract

In this paper, we study the divisibility of the function a(n) defined by [Formula: see text]. In particular, we prove certain "Ramanujan type congruences" for a(n) modulo powers of 3.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042110003241

Reference32 articles.

1. Distribution of the partition function modulo composite integers M

2. Congruence properties for the partition function

3. Arithmetic properties of the partition function

4. Encycl. Math. and Its Appl.;Andrews G. E.,1998

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