Ramanujan’s Conjecture and ℓ-Adic Representations

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 3 in The Mathematical Legacy of Srinivasa Ramanujan, 2013, pp 25-37 from Springer

Abstract: Abstract Ramanujan discovered some remarkable congruences satisfied by the τ-function. In retrospect, these congruences are now better understood via the theory of ℓ-adic representations. We present a short survey of these ideas and indicate the relationship between Ramanujan’s conjecture on the growth of τ(n) with the celebrated Weil conjectures, formulated by André Weil in 1949. These conjectures inspired the rapid development of modern algebraic geometry.

Keywords: Zeta Function; Modular Form; Elliptic Curve; Characteristic Polynomial; Elliptic Curf (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-81-322-0770-2_3

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DOI: 10.1007/978-81-322-0770-2_3

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