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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 ...
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 ...
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 ...
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.
Ramanujan (Original Motion Picture Soundtrack) is the soundtrack composed by Ramesh Vinayakam to the 2014 biographical film Ramanujan based on the life of Indian mathematician Srinivasa Ramanujan. The film, directed by Gnana Rajasekaran starred Abhinay Vaddi in the lead role and featured an ensemble cast of Suhasini Maniratnam , Bhama , Kevin ...
I would like to emphasize that the Dirichlet L-functions satisfy both of the condition (1) and (2), on the other hand, the Ramanujan L-function, i.e. the Ramanujan tau-function, one of Automorphic L-functions, does not satisfy (2) but (3), which is the difference between them.--Enyokoyama 14:11, 5 July 2014 (UTC)
George Andrews [14] showed that several of Ramanujan's fifth order mock theta functions are equal to quotients Θ(𝜏) / θ(𝜏) where θ(𝜏) is a modular form of weight 1 / 2 and Θ(𝜏) is a theta function of an indefinite binary quadratic form, and Dean Hickerson [15] proved similar results for seventh order mock theta ...
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