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The Mathematical Legacy of Srinivasa Ramanujan pp 39–66Cite as

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

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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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada

    M. Ram Murty

  2. Department of Mathematics, University of Toronto, Toronto, Ontario, Canada

    V. Kumar Murty

Authors
  1. M. Ram Murty
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  2. V. Kumar Murty
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Murty, M.R., Murty, V.K. (2013). The Ramanujan Conjecture from GL(2) to GL(n). In: The Mathematical Legacy of Srinivasa Ramanujan. Springer, India. https://doi.org/10.1007/978-81-322-0770-2_4

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