ISBN: 9780817630881 - arithmetic on modular curves (progress in mathematics, 20, band 20) (4 Ergebnisse)

Zustand: New. In English.

Paperback. Zustand: Brand New. reprint edition. 234 pages. 9.02x5.98x0.54 inches. In Stock.

Zustand: New. Series: Progress in Mathematics. Num Pages: 218 pages, black & white illustrations. BIC Classification: PBF. Category: (P) Professional & Vocational. Dimension: 229 x 152 x 13. Weight in Grams: 465. . 1982. 1982nd Edition. Paperback. . . . . Books ship from the US and Ireland.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.…