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Abstract: this paper is to discuss each of the Lambert series identities as well as to provide the arithmetical corollaries to which Ramanujan alluded. Several are related to the number of representations of an integer as a sum of squares or as a sum of triangular numbers. One of the most interesting identities yields a formula for the number of ways an integer can be represented as a sum of six triangular numbers. Although we expect that this formula is in the classical literature, we have been unable... (Update)
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0.9: The Remaining 40% Of Ramanujan's Lost Notebook - Berndt (Correct)
0.7: The Rogers-Ramanujan Continued Fraction - Berndt, Chan, Huang, Kang, Sohn.. (Correct)
0.7: Residue Theorem and Theta Function Identities - Liu (2001) (Correct)
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0.6: Some Theorems On The Rogers-Ramanujan Continued Fraction .. - Berndt, Huang, Sohn, Son (Correct)
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BibTeX entry: (Update)
@misc{ berndt-fragments,
author = "Bruce C. Berndt",
title = "Fragments by Ramanujan on Lambert Series",
url = "citeseer.ist.psu.edu/365398.html" }
Citations (may not include all citations):161 A Course of Modern Analysis (context) - Whittaker, Watson - 1966
110 Ramanujan's Notebooks (context) - Berndt - 1991
110 Ramanujan's Notebooks (context) - Berndt - 1998
24 Tata Institute of Fundamental Research (context) - Ramanujan, volumes - 1957
19 A cubic counterpart of Jacobi's identity and the AGM (context) - Borwein - 1991
14 The Lost Notebook and Other Unpublished Papers (context) - Ramanujan - 1988
12 Collected Papers (context) - Ramanujan - 1962
11 Ramanujan's theories of elliptic functions to alternative ba.. - Berndt, Bhargava et al. - 1995
10 Gauthier--Villars (context) - Cauchy, vol
7 Fundamenta Nova Theoriae Functionum Ellipticarum (context) - Jacobi
5 New infinite families of exact sums of squares formulas (context) - Milne - 1996
4 Integrable highest weight modules over affine superalgebras .. (context) - Kac, Wakimoto - 1994
4 On certain trigonometrical sums and their applications in th.. (context) - Ramanujan - 1918
2 New proofs of Ramanujan's partition identities for moduli 5 .. (context) - Chan - 1995
2 the equivalence of Ramanujan's partition identities and a co.. (context) - Chan - 1996
2 American Mathematical Society (context) - Son, of et al. - 1997
2 the representation of integers as sums of triangular numbers (context) - Ono, Robins et al. - 1995
2 Note on the Eisenstein series of \Gamma (context) - Kolberg - 1968
1 jointly published by the London Mathematical Society (context) - Berndt, Rankin et al. - 1995
1 Hecke series values of holomorphic cusp forms in the centre .. (context) - Bykovsky
1 Recherches sur diverses applications de l'analyse infinit'es.. (context) - Dirichlet
1 the modular equations of degree (context) - --C, On - 1994
1 M'emoire sur l'application du calcul des r'esidus au d'evelo.. (context) - Cauchy
1 the additive formulae of the theta functions and a collectio.. (context) - --C, On - 1994
1 Jacobi elliptic functions (context) - Milne, squares
1 Trait'e des Fonctions Elliptiques (context) - Legendre
1 Sum of six squares (context) - Liu
1 FRAGMENTS BY RAMANUJAN ON LAMBERT SERIES (context) - Carlitz, some et al. - 1953
Documents on the same site (http://www.math.uiuc.edu/~berndt/): More
Some Theta Function Identities Related To The Rogers-Ramanujan.. - Son (Correct)
Some Theorems On The Rogers-Ramanujan Continued Fraction .. - Berndt, Huang, Sohn, Son (Correct)
Ramanujan's Remarkable Product Of Theta-Functions - Berndt, Chan, Zhang (Correct)
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