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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 ...
In mathematics, Ramanujan's congruences are the congruences for the partition function p(n) discovered by Srinivasa Ramanujan: (+) ...
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 ...
Saraswathi of Rediff wrote, "Ramanujan is a brilliant film, a must watch" and gave the film 4/5. [20] Gautaman Bhaskaran of The Hindustan Times gave the film 3/5 stars and wrote, "The movie is a poignant look at the way a prodigy struggled and suffered in a penurious family, a mastermind whose mathematical wizardry invited ridicule and ...
See Winnie Li's survey on Ramanujan's conjecture and other aspects of number theory relevant to these results. [ 5 ] Lubotzky , Phillips and Sarnak [ 2 ] and independently Margulis [ 6 ] showed how to construct an infinite family of ( p + 1 ) {\displaystyle (p+1)} -regular Ramanujan graphs, whenever p {\displaystyle p} is a prime number and p ...
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).
Lafforgue's theorem implies the Ramanujan–Petersson conjecture that if an automorphic form for GL n (F) has central character of finite order, then the corresponding Hecke eigenvalues at every unramified place have absolute value 1.
L.A. Law: The Movie is a 2002 American made-for-television drama film based on the 1986–1994 television series L.A. Law which reunited most of the original cast, although not all prominent cast members returned, including Blair Underwood (Jonathan Rollins), Jimmy Smits (Victor Sifuentes), Amanda Donohoe (C.J. Lamb) and John Spencer (Tommy Mullaney).
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