Keyword

modular equations

Description: Modular equations are algebraic relations between modular functions, often studied in number theory and connected with elliptic functions and special series.

Primary topic: Advanced Mathematical Identities (64%)

Wikidata ID: wiki/Q6889716

OpenAlex ID: keywords/modular-equations

Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity

2011 · Jonathan M. Borwein, Peter Borwein · Medical Entomology and Zoology · 429

Modular Equations and Approximations to π

2000 · Lennart Berggren, Jonathan Borwein, et al. · Springer eBooks · 344

Basic Hypergeometric Series and Applications.

1990 · Ranjan Roy, Nathan J. Fine · American Mathematical Monthly · 327

Generalized elliptic integrals and modular equations

2000 · G.D. Anderson, S.-L. Qiu, et al. · Pacific Journal of Mathematics · 258

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Ueber die Transformation siebenter Ordnung der elliptischen Functionen

1878 · Felix Klein · Mathematische Annalen · 258

Collected papers of Srinivasa Ramanujan

1928 · Notes and Queries · 237

Ramanujan’s theories of elliptic functions to alternative bases

1995 · Bruce C. Berndt, S. Bhargava, et al. · Transactions of the American Mathematical Society · 185

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Proof of a conjecture of Ramanujan

1967 · A. O. L. Atkin · Glasgow Mathematical Journal · 136

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Polynomial Identities and Hauptmoduln

1981 · W. W. STOTHERS · The Quarterly Journal of Mathematics · 135

Ramanujan's Cubic Continued Fraction and an Analog of His "most Beautiful Identity"

2010 · HEI-CHI CHAN · International Journal of Number Theory · 126

Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi

1989 · J. M. Borwein, P. B. Borwein, et al. · American Mathematical Monthly · 117

Modular transformations and generalizations of several formulae of Ramanujan

1977 · Bruce C. Berndt · Rocky Mountain Journal of Mathematics · 115

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Ramanujan's Series for 1/π: A Survey

2009 · Nayandeep Deka Baruah, Bruce C. Berndt, et al. · American Mathematical Monthly · 108

MEDUSA--A Simulator for Modular Circuits

1982 · W.L. Engl, R. Laur, et al. · IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems · 104

Ramunujan's “Lost” Notebook III. The Rogers-Ramanujan continued fraction

1981 · George E Andrews · Advances in Mathematics · 98

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An Application of Modular Equations in Analysis Situs

1912 · Oswald Veblen · Annals of Mathematics · 95

Ramanujan's Theories of Elliptic Functions to Alternative Bases

1995 · Bruce C. Berndt, S. Bhargava, et al. · Transactions of the American Mathematical Society · 83

On Rationally Parametrized Modular Equations

2006 · Maier, Robert S. · arXiv (Cornell University) · 67

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Theta-function identities and the explicit formulas for theta-function and their applications

2004 · Jinhee Yi · Journal of Mathematical Analysis and Applications · 67

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Inequalities and infinite product formula for Ramanujan generalized modular equation function

2017 · Miao-Kun Wang, Yong-Min Li, et al. · The Ramanujan Journal · 64

On Ramanujan's cubic continued fraction

1995 · Heng Chan · Acta Arithmetica · 60

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On the hard-hexagon model and the theory of modular functions

1988 · G. S. Joyce · Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences · 53

Analogues of Ramanujan’s partition identities and congruences arising from his theta functions and modular equations

2011 · Nayandeep Deka Baruah, Kanan Kumari Ojah · The Ramanujan Journal · 52

Ramanujan-Göllnitz-Gordon Continued Fraction

1997 · Heng Huat Chan, Sen-Shan Huang · The Ramanujan Journal · 51

Weber's class invariants

1969 · B. J. Birch · Mathematika · 51

Works count: 987

Citation count: 7,423