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Satake (1966) reformulated the Ramanujan–Petersson conjecture in terms of automorphic representations for GL(2) as saying that the local components of automorphic representations lie in the principal series, and suggested this condition as a generalization of the Ramanujan–Petersson conjecture to automorphic forms on other groups. Another ...
The first two properties were proved by Mordell (1917) and the third one, called the Ramanujan conjecture, was proved by Deligne in 1974 as a consequence of his proof of the Weil conjectures (specifically, he deduced it by applying them to a Kuga-Sato variety).
⇒Ramanujan–Petersson conjecture Proposed by André Weil. Deligne's theorems completed around 15 years of work on the general case. 1975: Henryk Hecht and Wilfried Schmid: Blattner's conjecture: representation theory for semisimple groups: 1975: William Haboush: Mumford conjecture: geometric invariant theory: Haboush's theorem: 1976: Kenneth ...
As Murty's survey paper [1] notes, Ramanujan graphs "fuse diverse branches of pure mathematics, namely, number theory, representation theory, and algebraic geometry". These graphs are indirectly named after Srinivasa Ramanujan; their name comes from the Ramanujan–Petersson conjecture, which was used in a construction of some of these graphs.
Ramanujan–Petersson conjecture: a number of related conjectures that are generalizations of the original conjecture. Sato–Tate conjecture: also a number of related conjectures that are generalizations of the original conjecture.
Srinivasa Ramanujan Aiyangar [a] (22 December 1887 – 26 April 1920) was an Indian mathematician.Often regarded as one of the greatest mathematicians of all time, though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then ...
In mathematics, Ramanujan's congruences are the congruences for the partition function p(n) discovered by Srinivasa Ramanujan: (+) ...
Elliott–Halberstam conjecture; Functional equation (L-function) Chebotarev's density theorem; Local zeta function. Weil conjectures; Modular form. modular group; Congruence subgroup; Hecke operator; Cusp form; Eisenstein series; Modular curve; Ramanujan–Petersson conjecture; Birch and Swinnerton-Dyer conjecture; Automorphic form; Selberg ...