Get Automorphic Forms, Representation Theory and Arithmetic: PDF

By S. Gelbart, G. Harder, K. Iwasawa, H. Jaquet, N.M. Katz, I. Piatetski-Shapiro, S. Raghavan, T. Shintani, H.M. Stark, D. Zagier

On Shimura’s correspondence for modular varieties of half-integral weight.- interval integrals of cohomology periods that are represented by means of Eisenstein series.- Wave entrance units of representations of Lie groups.- On p-adic representations linked to ?p-extensions.- Dirichlet sequence for the gang GL(n).- Crystalline cohomology, Dieudonné modules and Jacobi sums.- Estimates of coefficients of modular kinds and generalized modular relations.- A comment on zeta capabilities of algebraic quantity fields.- Derivatives of L-series at s = 0.- Eisenstein sequence and the Riemann zeta function.- Eisenstein sequence and the Selberg hint formulation I.

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Extra resources for Automorphic Forms, Representation Theory and Arithmetic: Papers presented at the Bombay Colloquium 1979

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And [25], Cor. ) Here we profit from the fact that'" cannot be a trivial or a quadratic character. 2. At this point I want to give an idea of one of the main questions of this paper. 1). Let us assume that we have selected generators e+ M~ = {,p :a-+ R / ,p(gb -1) = ", (b),p (g) } by mapping ,p-+{g-+ ,p(g). g ·e+}. One knows that M~ and M"i are irreducible a-modules and they are isomorphic. p ,peg) = with w = 2 tis (wug) (0 1) is a non zero interwining operator ([25}, § 5). u£U. ) is isotypical.

At this point I want to give an idea of one of the main questions of this paper. 1). Let us assume that we have selected generators e+ M~ = {,p :a-+ R / ,p(gb -1) = ", (b),p (g) } by mapping ,p-+{g-+ ,p(g). g ·e+}. One knows that M~ and M"i are irreducible a-modules and they are isomorphic. p ,peg) = with w = 2 tis (wug) (0 1) is a non zero interwining operator ([25}, § 5). u£U. ) is isotypical. Let us denote the quotient field of R by K. For any", we pick the isotypical component ofM~ in H\r\X,K) and get a map H1(r\X,K)~--+M~® Kffi M~®K It follows from topological reasons that the image of the restriction map is of multiplicity one (namely!

And P. J. SALLY, "Intertwining Operators and Automorphic Fonns for the Metaplectic Group", Proc. , Vol. 4, pp. 1406-1410, April 1975. , "B-series and automorphic fonns", in Proc. Sym. , Vol. 33, 1979. 1. PIATETSKI-SHAPIRO, "A Counterexample to the Generalized Ramanujan Conjecture", in Proc. Symp. Pure. , Vo. , 1979. , Automorphic Forms on GL(2): Part II, Springer Lecture Notes, Vol. 278, 1972. , and R. P. LANGLANDS, Automorphic Forms on GL(2), Springer Lecture Notes, Vol. 114, 1970. , Automorphic Functions and the Reciprocity Law in a Number Field, Kyoto University Press, Kyoto, Japan, 1969.

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