Ramanujan and Transcendence

M. Ram Murty and V. Kumar Murty
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M. Ram Murty: Queen’s University, Department of Mathematics and Statistics
V. Kumar Murty: University of Toronto, Department of Mathematics

Chapter Chapter 6 in The Mathematical Legacy of Srinivasa Ramanujan, 2013, pp 97-107 from Springer

Abstract: Abstract In his 1916 memoir entitled “On certain arithmetic function,” Ramanujan considered the three fundamental Eisenstein series P,Q, and R. In that paper, he derived a system of nonlinear differential equations satisfied by them. These equations played a fundamental role in the 1996 work of Nesterenko who calculated the transcendence degree of the field generated by the special values of these Eisenstein series. In this chapter, we discuss the significance of this work in transcendental number theory.

Keywords: Modular Form; Eisenstein Series; Modular Function; Riemann Zeta Function; Mock Modular Form (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-81-322-0770-2_6

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