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The more general Ramanujan–Petersson conjecture for holomorphic cusp forms in the theory of elliptic modular forms for congruence subgroups has a similar formulation, with exponent (k − 1)/2 where k is the weight of the form.
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 [4] wrote down seven mock theta functions of order 6 in his lost notebook, and stated 11 identities between them, which were proved by Andrews and Hickerson. [29] Two of Ramanujan's identities relate φ and ψ at various arguments, four of them express φ and ψ in terms of Appell–Lerch series, and the last five identities express ...
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)
The Ramanujan machine is a specialised software package, developed by a team of scientists at the Technion: Israeli Institute of Technology, to discover new formulas in mathematics. It has been named after the Indian mathematician Srinivasa Ramanujan because it supposedly imitates the thought process of Ramanujan in his discovery of hundreds of ...
In mathematics, particularly q-analog theory, the Ramanujan theta function generalizes the form of the Jacobi theta functions, while capturing their general properties. In particular, the Jacobi triple product takes on a particularly elegant form when written in terms of the Ramanujan theta. The function is named after mathematician Srinivasa ...
The initial idea is usually attributed to the work of Hardy with Srinivasa Ramanujan a few years earlier, in 1916 and 1917, on the asymptotics of the partition function.It was taken up by many other researchers, including Harold Davenport and I. M. Vinogradov, who modified the formulation slightly (moving from complex analysis to exponential sums), without changing the broad lines.