Download PDF by Participants and Observers: 1975 U.S. - JAPAN SEMINAR - APPLICATIONS OF

By Participants and Observers

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By Participants and Observers

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Additional info for 1975 U.S. - JAPAN SEMINAR - APPLICATIONS OF AUTOMORPHIC FORMS TO NUMBER THEORY

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We s h a l l prove t h e following theorems : Theorem 1. t fi(r) - 1 + X(p)pk-l f o r every prime Theorem 2. (mod+a-1 . lying over 0. 1, Then, f o r each such t h a t ai(p) k We assume (mod 0 E 2) (i) k a if i s an even, p o s i t i v e i n t e g e r . SE 0 (mod R) = q. 2 Let Suppose t h e r e e x i s t s a c e r t a i n - 1 + X(p)pk-l f o r every prime of t p. number s a t i s f y i n g k s 0 K be any prime d i v i s o r o f there exists a certain -2i(B k s x and be an odd prime f a c t o r of t h e numerator of p.

3 ) ; + P + (Th. 4). A l l t h e s t e p s are r o u t i n e e x c e p t t h e one : (L. 21, ( 2)*(~h. 3). and References [l] A. 0. L. Atkin, and J. Lehner, (1970) 134-160. [2] M. E i c h l e r , Uber d i e D a r s t e l l b a r k e i t von Modulformen durch T h e t a r e i h e n , J. r e i n e und angew. Math. 195(1956) 156-171. I 131 Hecke Operators on G ( m ) , Math. * -, I Quadratische Formen und Modulfunktionen, Acta A r i t h . 4 (1958) 217-239. [4] The b a s i s problem f o r modular forms and t h e t r a c e s of t h e Hecke , o p e r a t o r s , L e c t u r e Notes i n Math.

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1975 U.S. - JAPAN SEMINAR - APPLICATIONS OF AUTOMORPHIC FORMS TO NUMBER THEORY by Participants and Observers


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