Arithmetic on Modular Curves

Language: English

Published by Birkhäuser, Birkhäuser Jan 1982, 1982

0817630880 / 9780817630881

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This item is printed on demand - Print on Demand Titel. Neuware -One of the most intriguing problems of modern number theory is to relate the arithmetic of abelian varieties to the special values of associated L-functions. A very precise conjecture has been formulated for elliptic curves by Birc~ and Swinnerton-Dyer and generalized to abelian varieties by Tate. The numerical evidence is quite encouraging. A weakened form of the conjectures has been verified for CM elliptic curves by Coates and Wiles, and recently strengthened by K. Rubin. But a general proof of the conjectures seems still to be a long way off. A few years ago, B. Mazur [26] proved a weak analog of these c- jectures. Let N be prime, and be a weight two newform for r 0 (N) . For a primitive Dirichlet character X of conductor prime to N, let i f (X) denote the algebraic part of L (f , X, 1) (see below). Mazur showed in [ 26] that the residue class of Af (X) modulo the 'Eisenstein' ideal gives information about the arithmetic of Xo (N). There are two aspects to his work: congruence formulae for the values Af(X) , and a descent argument. Mazur's congruence formulae were extended to r 1 (N), N prime, by S. Kamienny and the author [17], and in a paper which will appear shortly, Kamienny has generalized the descent argument to this case.Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 236 pp. Englisch.…

Seller Inventory # 9780817630881

Title
Arithmetic on Modular Curves
Author
G. Stevens
Publisher
Birkhäuser, Birkhäuser Jan 1982
Publication year
1982
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
0817630880
ISBN 13
9780817630881
Item weight
349 grams
Dimensions
229x152x13 mm

buchversandmimpf2000

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