By Lin Weng, Masanobu Kaneko
This priceless quantity collects papers written through a few of the world's best specialists on L-functions. It not just covers a variety of issues from algebraic and analytic quantity theories, automorphic varieties, to geometry and mathematical physics, but in addition treats the speculation as a complete. The contributions replicate the most recent, so much complicated and most vital elements of L-functions. particularly, it comprises Hida's lecture notes on the convention and on the Eigen type semester in Harvard collage and Weng's targeted account of his works on excessive rank zeta features and non-abelian L-functions.
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Additional info for The Conference on L-functions: Fukuoka, Japan, 18-23 February 2006
Example text
Then ap : Dv> -» K is a homomorphism. [p, FP']\ylp (\ogp(yp>YX ap([yp>, Fv\))p^p) J. The above value is independent of the choice of the basis {cp}p. 4 (generalizing those of Wiles [W] and Taylor-Wiles [TW]), we always have R a K[[Xp]]. In general, assuming the following two conditions: (ai) p = (PF mod m^) is absolutely irreducible over Gal(Q/F[jUp]); (ds) pss has a non-scalar value over Gal(F p /F p ) for all prime factors p\p, by using a result of Fujiwara (see [Fu] and [Ful]), we can prove R = K[[Xp]]p\p.
Indicating one of +, - , eye or "nothing". When nothing is attached, it refers to the object for the full multiple Zp-extension MM. p. , this action factors through Gal(MAM^,/M). Then we look into the compact p-profinite T ? module: XJ[ 3, H = SelF(V), and {cp}p gives a basis of H over K. We have 6([u, F p ]) = (1 + Xp)iogp(«)/iogp(r) for u e 0 x = z x W r i t i n g /-flp(o-) C (ff ) = '" l 0 * \ i Pl r) ' fl,(