= c for some integers a, b, c with ab 6= 0, has only finitely many integer solutions. Stoll & Tichy proved more generally that if a, b, c âˆˆ Q and ab 6= 0, then for m > n â‰¥ 3, the above equation hasâ€¦ (More)

Let k be a global field and let kv be the completion of k with respect to v, a non-archimedean place of k. Let G be a connected, simply-connected algebraic group over k, which is absolutely almostâ€¦ (More)

Elementary proofs abound: the first identity results from choosing x = y = 1 in the binomial expansion of (x+y). The second one may be obtained by comparing the coefficient of x in the identity (1 +â€¦ (More)

In this article we obtain a general polynomial identity in k variables, where k â‰¥ 2 is an arbitrary positive integer. We use this identity to give a closed-form expression for the entries of theâ€¦ (More)

In the 1960â€™s Noboru Iwahori and Hideya Matsumoto, Eiichi Abe and Kazuo Suzuki, and Michael Stein discovered that Chevalley groups G = G(Î¦, R) over a semilocal ring admit remarkable Gaussâ€¦ (More)

Let K/F be a cyclic extension of prime degree l over a number field F . If F has class number coprime to l, we study the structure of the l-Sylow subgroup of the class group of K. In particular, whenâ€¦ (More)

faculty there in 1969. He has held other faculty positions and visiting positions at many universities and research institutes around the world. He has written more than 1000 papers and hasâ€¦ (More)

Some problems on algebraic groups over global fields like the congruence subgroup problem involve the determination of topological central extensions of the adelic group which, in turn, leadsâ€¦ (More)