The Ramanujan Conjecture from GL(2) to GL(n)

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 4 in The Mathematical Legacy of Srinivasa Ramanujan, 2013, pp 39-66 from Springer

Abstract: Abstract Ramanujan’s conjectures regarding the τ-function represent part of a larger spectrum of conjectures, first in the setting of automorphic forms attached to GL(2) and generally to GL(n). In this chapter, we trace this development highlighting what is known and what is unknown. In this way, Ramanujan’s 1916 memoir becomes part of a larger theory, now called the Langlands program.

Keywords: Ramanujan Conjecture; Selberg Eigenvalue Conjecture; Maass Forms; Kloosterman Sums; Kloosterman-Selberg Zeta Function (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_4

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DOI: 10.1007/978-81-322-0770-2_4

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