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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 ...
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 ...
Download as PDF; Printable version; In other projects ... (1917) and the third one, called the Ramanujan conjecture, ... Ramanujan's L-function is defined by = ...
Srinivasa Ramanujan first discovered that the partition function has nontrivial patterns in modular arithmetic, now known as Ramanujan's congruences. For instance, whenever the decimal representation of n ends in the digit 4 or 9, the number of partitions of n will be divisible by 5.
Spectrum and Ramanujan conjectures [ edit ] The Ramanujan conjecture for automorphic forms on G L ( 2 ) {\displaystyle \mathrm {GL} (2)} over a number field would imply that for any congruence cover of an arithmetic three-manifold (derived from a quaternion algebra) the spectrum of the Laplace operator is contained in [ 1 , + ∞ ...
By Maggie Fick. LONDON (Reuters) - An official Palestinian tally of direct deaths in the Israel-Hamas war likely undercounted the number of casualties by 41% through the middle of 2024 as the Gaza ...
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Allen finished throwing 22-of-37 for 342 yards in the loss for the Bills. He had 82 rushing yards on 10 carries to lead the team on the ground, too.