algebraic groups and number theory - platonov & rapinchuk

... suitable i in Z and c in L. Writing t = s(gic ) -& apos;, we have P = tgicLc-lg-it-' = tLt-l and NrdDIK(t) = 1. Consequently, x E ~(')y-l c tP1 L(')~L('). Q.E.D. ... problems and the well-known Kneser-Tits conjecture in the theory of algebraic groups, see 57.2. Platonov solved the Tanaka-Artin problem in 1975 and found 28 Chapter 1....

Ngày tải lên: 31/03/2014, 16:21

Ngày tải lên: 27/03/2014, 11:48

... while the sequence {A 2n−1 } is strictly decreasing, i.e., A 0 < A 2 < ··· < A 2m < ··· < A 2n−1 < ··· < A 3 < A 1 . Theorem 1.35. The convergents of the infinite continued ... there must be a factorization n 0 = uv with u, v ∈ N 0 and u, v = 1. Then we have 1 < u < n 0 and 1 < v < n 0 , hence u, v /∈ S and so there are factorizations u = p 1 ···p r ,...

Ngày tải lên: 31/03/2014, 16:21

... e k 2 ∧···e k n with k 1 >k 2 > ···k n > 0and e k =exp(−ikx), with half-integral and integral k, resp. The Z 2 degree of such a vector is 0 for even n and 1 for odd n. The two-dimensional space ... ⊕ h+ ¯ h≤d F (h, ¯ h )and demands that for some N and sufficiently large d the dimension of these 82 Werner Nahm spaces is smaller than for the theory F N ⊗ ¯ F N of N holomorphic...

Ngày tải lên: 12/02/2014, 16:20

... work of Conrey-Ghosh, Conrey-Gonek, Duke-Friedlander-Iwaniec, Kowalski-Michel-Vanderkam, Ju- tila, Motohashi, Ivic, Soundararajan, Rubinstein, and others on moments of families of L-functions which ... (1996) 147 2-1 475. 22. E. Bogomolny and J.P. Keating, Random Matrix Theory and the Riemann Zeros I: , Nonlinearity 8 (1995) 111 5-1 131; Random Matrix Theory and the Riemann Ze...

Ngày tải lên: 12/02/2014, 17:20

... Grassmannian remains a complex algebraic object. *I. Mirkovi´c and K. Vilonen were supported by NSF and the DARPA grant HR001 1-0 4- 1-0 031. LANGLANDS DUALITY AND ALGEBRAIC GROUPS] 123 We now argue using ... Geometric Langlands duality and representations of algebraic groups over commutative rings By I. Mirkovi´c and K. Vilonen* LANGLANDS DUALITY AND...

Ngày tải lên: 06/03/2014, 08:21

... q = 1 and r = 986. Notice that if a natural number d divides both 2261 and 1275, then d divides their difference 986 and d still divides 1275. On the other hand, if d divides both 1275 and 986, ... nonempty because 0 ∈ Q and Q is bounded because a −bn < 0 for all n > a/b. Let q be the largest element of Q. Then r = a − bq < b, otherwise q + 1 would also be in Q. Thus q an...

Ngày tải lên: 07/03/2014, 16:20

... y, and n > 0, then 2 - ylx" - y". 2 - 11s" - 1, In particular, if y = 1, and, if y = -y, and n is odd, (n is odd). (13b) 2 + ylz" + y", ... 1 Qn b qo +- 1 q1 + - q2 + -, and, specifically, Similarly from (e) above, we have 3x2 - lox + 7 - 9 - x3 - 5s' + 7~ - 3...

Ngày tải lên: 15/03/2014, 16:03