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Download as PDF; Printable version ... Redirect page. Redirect to: Ramanujan–Petersson conjecture; ... Text is available under the Creative Commons Attribution ...
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.
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 ...
Zhang in Berkeley in 2021. Ruixiang Zhang is a mathematician specializing in Euclidean harmonic analysis, analytic number theory, geometry and additive combinatorics.He is an assistant professor in the Department of Mathematics at University of California, Berkeley. [1]
Conjecture Field Comments Eponym(s) Cites 1/3–2/3 conjecture: order theory: n/a: 70 abc conjecture: number theory: ⇔Granville–Langevin conjecture, Vojta's conjecture in dimension 1 ⇒Erdős–Woods conjecture, Fermat–Catalan conjecture Formulated by David Masser and Joseph Oesterlé. [1] Proof claimed in 2012 by Shinichi Mochizuki: n/a ...
At Purdue University he became in 1977 an assistant professor, in 1982 an associate professor, and 1986 a full professor. There he since 2001 is a Distinguished Professor. He returned to the Institute for Advanced Study in 1983–1984, in 1990–1991, in October–November 1999, and in several other brief visits.
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 ...