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Distribution of powers of the partition function modulo ℓ^j

Brown, Jim L. and Li, Yingkun (2009) Distribution of powers of the partition function modulo ℓ^j. Journal of Number Theory, 129 (10). pp. 2557-2568. ISSN 0022-314X.

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In this paper we study Newman's conjecture for powers of the partition function. While this conjecture is known for powers of primes ℓ that are not exceptional for the power under consideration, it is an open problem for exceptional primes. We settle this conjecture in many cases for small powers of the partition function by generalizing results of Ono and Ahlgren. It should be noted our method requires a case by case examination of each power and does not yield a general method for dealing with different powers simultaneously.

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Additional Information:© 2009 Elsevier. Received 27 October 2008; revised 17 December 2008. Communicated by James W. Cogdell. Available online 13 February 2009. Supported by a Summer Undergraduate Research Fellowship at California Institute of Technology and the John and Maria Laffin Trust.
Funding AgencyGrant Number
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
John and Maria Laffin TrustUNSPECIFIED
Subject Keywords:Newman's conjecture; Partitions; Modular forms
Issue or Number:10
Classification Code:Mathematical subject codes: 11F33; 11P83
Record Number:CaltechAUTHORS:20090817-144816424
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Official Citation:Jim L. Brown, Yingkun Li, Distribution of powers of the partition function modulo lj, Journal of Number Theory, Volume 129, Issue 10, October 2009, Pages 2557-2568, ISSN 0022-314X, DOI: 10.1016/j.jnt.2008.12.007.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15108
Deposited By: George Porter
Deposited On:08 Sep 2009 17:27
Last Modified:03 Oct 2019 00:55

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