In mathematics, the Arthur conjectures refer to a set of conjectures proposed by James Arthur in 1989. These conjectures pertain to the properties of automorphic...

number of related conjectures that are generalizations of the original conjecture. Sato–Tate conjecture: also a number of related conjectures that are generalizations...

unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem...

to reduce the Ramanujan conjecture to the Weil conjectures that he later proved.　The more general Ramanujan–Petersson conjecture for holomorphic cusp forms...

1351–1359. doi:10.1112/S0010437X09003959. Rubin, Karl (1991). "The 'main conjectures' of Iwasawa theory for imaginary quadratic fields". Inventiones Mathematicae...

theta-series had been developed. The conjectures have evolved since Langlands first stated them. Langlands conjectures apply across many different groups...

In mathematics, the Hodge conjecture is a major unsolved problem in algebraic geometry and complex geometry that relates the algebraic topology of a non-singular...

monograph on a geometric approach to the Langlands classification and Arthur's conjectures in the real case. He completed his Ph.D. at Yale University under...

the Langlands conjecture for general linear groups over function fields. Maass wave form Harmonic Maass form Arthur's conjectures Arthur, James (1981)...

Interpretation of Nature and the Psyche. This culminated in the Pauli–Jung conjecture. Jung and Pauli's view was that, just as causal connections can provide...

Pollock's conjectures are closely related conjectures in additive number theory. They were first stated in 1850 by Sir Frederick Pollock, better known...

for research on the Langlands program. He also introduced the Arthur conjectures. Arthur was elected a Fellow of the Royal Society of Canada in 1981 and...

} with a specified constant c. Neal Koblitz (1988) provided detailed conjectures for the case of a prime number q of points on Ep, motivated by elliptic...

that solved it opened up a new way of attacking one of the big webs of conjectures of contemporary mathematics called the Langlands Program, which as a...

-P. Serre, Facteurs locaux des fonctions zêta des variétés algébriques (définitions et conjectures), 1969/1970, Sém. Delange–Pisot–Poitou, exposé 19...

rights movement". In his book Trinity of Passion, author Alan M. Wald conjectures that Miller was "a member of a writer's unit of the Communist Party around...

combinatorics, the proof of the Dowling–Wilson conjecture for geometric lattices, the proof of the Heron–Rota–Welsh conjecture for matroids, the development of the...

of the non-Newtonian complexity of quantum computation. NLTS and qPCP conjectures posit the near-infinite complexity involved in predicting the outcome...

conjecture to the Farrell–Jones conjecture (compare ). Farrell, F. Thomas, Jones, Lowell E., Isomorphism conjectures in algebraic K-theory, Journal of...

and Tao was incomplete, as it was conditioned upon unproven conjectures. Those conjectures were proved in later work of Green, Tao, and Tamar Ziegler.[GTZ12]...

prime conjecture is equivalent to P(2); and in fact it has been conjectured that P(k) holds for all even integers k. While these stronger conjectures remain...

the case with some other past conjectures, such as with Skewes' number, and it could not be ruled out in this conjecture.) The strategy that ultimately...

(with Collingwood) that Arthur was historical, said "It is inconceivable that Gildas ... should not have mentioned Arthur's part ..." (that is, if he...

Allyn (September 2006). "Conjectures no more? Consensus forming on the proof of the Poincaré and geometrization conjectures" (PDF). Notices of the American...

the product of local L-factors given by the local Langlands conjectures. The conjecture states that the following are equivalent: The period interval...

superstring theory, the extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau manifold, which led to...

situation ( P S 1 {\displaystyle \mathrm {PS} _{1}} ), a number of competing conjectures, or tentative theories ( T T {\displaystyle \mathrm {TT} } ), are systematically...

has what is called the "Bertrand Conjecture" of −1. This means that if firm A increases its output, it conjectures that firm B will reduce its output...

unique games conjecture. Khot received the 2014 Rolf Nevanlinna Prize by the International Mathematical Union and received the MacArthur Fellowship in...

a recurring pattern of three killings based on traumatic events during Arthur's childhood. In the series, Mitchell is portrayed by John Lithgow. Lithgow's...