Modular Equations in Ramanujan’s Lost Notebook

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Abstract

Ramanujan recorded several hundred modular equations in his three notebooks [7]; no other mathematician has ever discovered nearly so many. Complete proofs for all the modular equations in Ramanujan’s three notebooks can be found in Berndt’s books [1]–[3]. In particular, Chapters 19–21 in Ramanujan’s second notebook are almost exclusively devoted to modular equations. Ramanujan used modular equations to evaluate class invariants, certain q-continued fractions including the Rogers-Ramanujan continued fraction, theta-functions, and certain other quotients and products of theta-functions and eta-functions [3].
Original languageEnglish (US)
Title of host publicationNumber Theory
EditorsR P Bambah, V C Dumir, R J Hans-Gill
PublisherBirkhäuser/Springer, Cham
Pages55-74
Number of pages20
ISBN (Electronic)978-93-86279-02-6
ISBN (Print)978-81-85931-23-4
DOIs
StatePublished - 2000

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