Mohlo by se vám také líbit

Více informací o knize Arithmetic on Modular Curves

• Parametry knihy
• Anotace
• Oblíbené z jiného soudku

Nákupem získáte 135 bodů

Anotace knihy

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.

Parametry knihy

Zařazení knihy Knihy v angličtině Mathematics & science Mathematics Algebra

• Plný název: Arithmetic on Modular Curves
• Autor: G. Stevens
• Jazyk: Angličtina
• Vazba: Brožovaná
• Počet stran: 217
• EAN: 9780817630881
• ISBN: 0817630880
• ID: 02643055
• Nakladatelství: Birkhauser Boston Inc
• Hmotnost: 348 g
• Rozměry: 230 × 153 × 18 mm

Oblíbené z jiného soudku

---

---

---