عنوان

Arithmetic on Modular Curves

شابک

9780817630881

شابک

9781468491654

شماره

b401767

عنوان اصلي

Arithmetic on Modular Curves

نام عام مواد

[Book]

نام نخستين پديدآور

by Glenn Stevens.

محل نشرو پخش و غیره

Boston, MA :

نام ناشر، پخش کننده و غيره

Birkhäuser Boston,

تاریخ نشرو بخش و غیره

1988.

عنوان فروست

Progress in Mathematics ;

مشخصه جلد

20

متن يادداشت

1. Background -- 1.1. Modular Curves -- 1.2. Hecke Operators -- 1.3. The Cusps -- 1.4. $ $ % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf % gDOjdaryqr1ngBPrginfgDObcv39gaiuqacqWFtcpvaaa!41F4! \mathbb{T} $ $-modules and Periods of Cusp Forms -- 1.5. Congruences -- 1.6. The Universal Special Values -- 1.7. Points of finite order in Pic0(X(?)) -- 1.8. Eisenstein Series and the Cuspidal Group -- 2. Periods of Modular Forms -- 2.1. L-functions -- 2.2. A Calculus of Special Values -- 2.3. The Cocycle ?f and Periods of Modular Forms -- 2.4. Eisenstein Series -- 2.5. Periods of Eisenstein Series -- 3. The Special Values Associated to Cuspidal Groups -- 3.1. Special Values Associated to the Cuspidal Group -- 3.2. Hecke Operators and Galois Modules -- 3.3. An Aside on Dirichlet L-functions -- 3.4. Eigenfunctions in the Space of Eisenstein Series -- 3.5. Nonvanishing Theorems -- 3.6. The Group of Periods -- 4. Congruences -- 4.1. Eisenstein Ideals -- 4.2. Congruences Satisfied by Values of L-functions -- 4.3. Two Examples: X1(13), X0(7,7) -- 5. P-adic L-functions and Congruences -- 5.1. Distributions, Measures and p-adic L-functions -- 5.2. Construction of Distributions -- 5.3. Universal measures and measures associated to cusp forms -- 5.4. Measures associated to Eisenstein Series -- 5.5. The Modular Symbol associated to E -- 5.6. Congruences Between p-adic L-functions -- 6. Tables of Special Values -- 6.1. X0(N), N prime ? 43 -- 6.2. Genus One Curves, X0(N) -- 6.3. X1(13), Odd quadratic characters.

بدون عنوان

0

متن يادداشت

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.

شماره استاندارد بين المللي کتاب و موسيقي

9780817630881

عنوان

Springer eBooks

موضوع مستند نشده

Mathematics.

مستند نام اشخاص تاييد نشده

Stevens, Glenn.

مستند نام تنالگان تاييد نشده

SpringerLink (Online service)

تاريخ عمليات

20190304170803.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y