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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.
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1974 Ramanujan conjecture and the Weil conjectures. While Deligne's final paper proving these conjectures were "only" about 30 pages long, it depended on background results in algebraic geometry and étale cohomology that Deligne estimated to be about 2000 pages long. 1974 4-color theorem. Appel and Haken's proof of this took 139 pages, and ...
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.
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 ...
President Joe Biden ordered a national day of mourning in January and flags to be displayed at half-staff following President Jimmy Carter's death.
When you’re flying across time zones or staying up late exploring new destinations, lack of sleep can leave you feeling groggy and irritable. Fortunately, there’s one nutrient that can help ...
Epps, 51, also faced an internal affairs investigation into her overtime, sources said. Records showed that last year she worked nearly 1,627 hours of overtime on top of her regular shift, or an ...