A fundamental modular identity and some applications
Authors:
Richard Blecksmith, John Brillhart and Irving Gerst
Journal:
Math. Comp. 61 (1993), 8395
MSC:
Primary 11P83; Secondary 05A19, 11F11
MathSciNet review:
1197509
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Abstract: We prove a sixparameter identity whose terms have the form , where . This identity is then used to give a new proof of the familiar Ramanujan identity , where and . Two other identities, called "balanced identities", are also established through its use.
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Richard
Blecksmith, John
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Richard
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Gerst, Some infinite product
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Richard
Blecksmith, John
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Gerst, On a certain (mod 2) identity and a
method of proof by expansion, Math. Comp.
56 (1991), no. 194, 775–794. MR 1068825
(91j:11087), http://dx.doi.org/10.1090/S00255718199110688252
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, A general formula for balanced identities of a simple type, Abstracts Amer. Math. Soc. 13 (1992), 504.
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 [1]
 B. J. Birch, A look back at Ramanujan's notebooks, Math. Proc. Cambridge Philos. Soc. 78 (1975), 7379. MR 0379372 (52:277)
 [2]
 R. Blecksmith, J. Brillhart, and I. Gerst, Parity results for certain partition functions and identities similar to theta function identities, Math. Comp. 48 (1987), 2938. MR 866096 (87k:11113)
 [3]
 , Some infinite product identities, Math. Comp. 51 (1988), 301314. MR 942157 (89f:05017)
 [4]
 , On a certain identity and a method of proof by expansion, Math. Comp. 56 (1991), 775794. MR 1068825 (91j:11087)
 [5]
 , A general formula for balanced identities of a simple type, Abstracts Amer. Math. Soc. 13 (1992), 504.
 [6]
 D. Bressoud, Proof and generalization of certain identities conjectured by Ramanujan, PhD Thesis, Temple University, Philadelphia, PA, 1977.
 [7]
 S. Ramanujan, Algebraic relations between certain infinite products, Collected Papers of Srinivasa Ramanujan, Chelsea, New York, 1962, p. 231. MR 2280872
 [8]
 S. Robins, Arithmetic properties of modular forms, PhD Thesis, University of California, Los Angeles, CA, 1991.
 [9]
 L. J. Rogers, On a type of modular relation, Proc. London Math. Soc. (2) 19 (1921), 387397.
 [10]
 G. N. Watson, Proof of certain identities in combinatory analysis, J. Indian Math. Soc. 20 (1933), 5769.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718199311975097
PII:
S 00255718(1993)11975097
Keywords:
Triple and quintuple product,
modular identity,
balanced and identity
Article copyright:
© Copyright 1993
American Mathematical Society
