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Convolution congruences for the partition function
Author(s):
Sharon
Anne
Garthwaite
Journal:
Proc. Amer. Math. Soc.
135
(2007),
13-20.
MSC (2000):
Primary 11P83;
Secondary 11F11
Posted:
June 19, 2006
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Abstract:
Ahlgren and Boylan recently proved the uniqueness of the Ramanujan congruences for the primes  ,  , and  by using the modularity of a certain partition function. Here we use their result to find universal congruences, of a different type, which hold for the partition function modulo all primes  .
References:
-
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- Scott Ahlgren and Matthew Boylan, Arithmetic properties of the partition function, Invent. Math. 153 (2003), no. 3, 487-502. MR 2000466 (2004e:11115)
- [And98]
- George E. Andrews, The theory of partitions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1998. MR 1634067 (99c:11126)
- [AO01]
- Scott Ahlgren and Ken Ono, Addition and counting: the arithmetic of partitions, Notices Amer. Math. Soc. 48 (2001), no. 9, 978-984. MR 1854533 (2002e:11136)
- [CKO05]
- Youngju Choie, Winfried Kohnen, and Ken Ono, Linear relations between modular form coefficients and non-ordinary primes, Bull. London Math. Soc. 37 (2005), no. 3, 335-341. MR 2131386 (2005m:11081)
- [Kob93]
- Neal Koblitz, Introduction to elliptic curves and modular forms, Graduate Texts in Mathematics, vol. 97, Springer-Verlag, New York, 1993. MR 1216136 (94a:11078)
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Additional Information:
Sharon
Anne
Garthwaite
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email:
garthwai@math.wisc.edu
DOI:
10.1090/S0002-9939-06-08443-7
PII:
S 0002-9939(06)08443-7
Received by editor(s):
July 5, 2005
Received by editor(s) in revised form:
July 25, 2005
Posted:
June 19, 2006
Additional Notes:
This research was supported by the University of Wisconsin Madison NSF VIGRE program
Communicated by:
Ken Ono
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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