Analogues of Jacobi's two-square theorem: an informal account

Melham, R

Analogues of Jacobi's two-square theorem: an informal account

Melham, R

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Publisher:: State University of West Georgia
Publication Type:: Journal Article
Citation:: Integers, 2010, 10 pp. 83 - 100
Issue Date:: 2010-01

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Field	Value	Language
dc.contributor.author	Melham, R	en_US
dc.date.issued	2010-01	en_US
dc.identifier.citation	Integers, 2010, 10 pp. 83 - 100	en_US
dc.identifier.issn	1553-1732	en_US
dc.identifier.uri	http://hdl.handle.net/10453/14526
dc.description.abstract	Jacobi's two-square theorem states that the number of representations of a positive integer k as a sum of two squares, counting order and sign, is 4 times the surplus of positive divisors of k congruent to 1 modulo 4 over those congruent to 3 modulo 4. In this paper we give numerous identities, each of which yields an analogue of Jacobi's result. Our identities are drawn from a much larger list, and involve polygonal numbers. The formula for the nth k-gonal number is	en_US
dc.publisher	State University of West Georgia	en_US
dc.relation.ispartof	Integers	en_US
dc.title	Analogues of Jacobi's two-square theorem: an informal account	en_US
dc.type	Journal Article
utslib.citation.volume	10	en_US
utslib.for	0101 Pure Mathematics	en_US
utslib.for	0802 Computation Theory and Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
utslib.copyright.status	open_access
pubs.consider-herdc	true	en_US
pubs.volume	10	en_US

Abstract:

Jacobi's two-square theorem states that the number of representations of a positive integer k as a sum of two squares, counting order and sign, is 4 times the surplus of positive divisors of k congruent to 1 modulo 4 over those congruent to 3 modulo 4. In this paper we give numerous identities, each of which yields an analogue of Jacobi's result. Our identities are drawn from a much larger list, and involve polygonal numbers. The formula for the nth k-gonal number is

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