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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.
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.
In mathematics, Ramanujan's congruences are the congruences for the partition function p(n) discovered by Srinivasa Ramanujan: (+) (), (+) (), (+) ().In plain words, e.g., the first congruence means that If a number is 4 more than a multiple of 5, i.e. it is in the sequence
In number theory, a branch of mathematics, Ramanujan's ternary quadratic form is the algebraic expression x 2 + y 2 + 10z 2 with integral values for x, y and z. [ 1 ] [ 2 ] Srinivasa Ramanujan considered this expression in a footnote in a paper [ 3 ] published in 1916 and briefly discussed the representability of integers in this 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 ...
The remaining five Australians from the infamous “Bali Nine” drug gang are “relieved and happy” to be home after Canberra struck a deal with Jakarta to end their two decades of imprisonment.
Tariff threats, drug pricing will be 2 key pharma issues during Trump's first year. Food. Food. Southern Living. Costco fans say this cake is 'worth its weight in gold' Food. Southern Living.
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