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On congruence properties of 
Author(s):
Brandt
Kronholm
Journal:
Proc. Amer. Math. Soc.
133
(2005),
2891-2895.
MSC (2000):
Primary 05A17, 11P83
Posted:
April 25, 2005
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Abstract:
In the late 19th century, Sylvester and Cayley investigated the properties of the partition function  . This function enumerates the partitions of a non-negative integer  into exactly  parts. Here we investigate the congruence properties of such functions and we obtain several infinite classes of Ramanujan-type congruences.
References:
- 1.
- G. E. Andrews, Partitions: At the interface of q-series and modular forms, Ramanujan Journal, 7 (2003), 385-400. MR 2035813 (2004j:11121)
- 2.
- A. O. L. Atkin, Proof of a conjecture of Ramanujan, Glascow Math. J., 8 (1967), 14-32.MR 0205958 (34:5783)
- 3.
- H. Gupta, E. E. Gwyther and J. C. P. Miller, Tables of Partitions, Royal Soc. Math. Tables, Vol. 4, Cambridge University Press, Cambridge, 1958.
- 4.
- K. Ono, Distribution of the partition function modulo m, Annals of Math. 151 (2000), 293-307. MR 1745012 (2000k:11115)
- 5.
- S. Ramanujan, Collected Papers, Cambridge University Press, London, 1927; reprinted: A. M. S. Chelsea, 2000 with new preface and extensive commentary by B. Berndt.
- 6.
- G. N. Watson, Ramanujan's Vermutung über Zerfällungsanzahlen, J. reine und angew. Math 179 (1938), 97-128.
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Additional Information:
Brandt
Kronholm
Affiliation:
Department of Mathematics, Penn State University, University Park, Pennsylvania 16802
Address at time of publication:
Department of Mathematics, University at Albany, Albany, New York 12222
Email:
kronholm@math.psu.edu
DOI:
10.1090/S0002-9939-05-07972-4
PII:
S 0002-9939(05)07972-4
Keywords:
Partition,
congruence,
generating function,
Ramanujan
Received by editor(s):
June 9, 2004
Posted:
April 25, 2005
Communicated by:
David E. Rohrlich
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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