# Download e-book for kindle: A 2-extension of the field of rational numbersof rational by Tsvetkov V. M.

By Tsvetkov V. M.

Similar number theory books

New PDF release: Algebraische Zahlentheorie (Springer-Lehrbuch Masterclass)

Algebraische Zahlentheorie: eine der traditionsreichsten und aktuellsten Grunddisziplinen der Mathematik. Das vorliegende Buch schildert ausführlich Grundlagen und Höhepunkte. Konkret, sleek und in vielen Teilen neu. Neu: Theorie der Ordnungen. Plus: die geometrische Neubegründung der Theorie der algebraischen Zahlkörper durch die "Riemann-Roch-Theorie" vom "Arakelovschen Standpunkt", die bis hin zum "Grothendieck-Riemann-Roch-Theorem" führt.

Read e-book online Selected Chapters of Geomety, Analysis and Number Theory PDF

The purpose of this publication is to offer brief notes or articles, in addition to experiences on a few themes of Geometry, research, and quantity conception. the fabric is split into ten chapters: * Geometry and geometric inequalities; * Sequences and sequence of actual numbers; * certain numbers and sequences of integers; * Algebraic and analytic inequalities; * Euler gamma functionality; * capacity and suggest worth theorems; * useful equations and inequalities; * Diophantine equations; * mathematics capabilities; * Miscellaneous subject matters.

Additional resources for A 2-extension of the field of rational numbersof rational numbers

Sample text

Let x' = bx + d and define a cubic in x' with Zc2 J coefficients by a'x'3 + b'x'2 + e'x' + d' 1 = 4(ax 3 + bx2 + ex + d- (bx + d) 2) , then c' ;/= d' mod 2. (5) If E has stable reduction modulo p but does not have good reduction, then E is said to have multiplicative reduction mod­ ulo p. If E does not have stable reduction, E is said to have additive reduction modulo p. Suppose E has stable reduction modulo an odd prime p. Among the defining equations of E satisfying ( 1 . 8 ) , one of them satisfies ( l .

Define a natural right action of the group GL 2 (Z/NZ) on the functors M (N) and M (N) as follows. For

MODULAR FORMS Arithmetically, the solution to the same problem is the link be­ tween elliptic curves and modular forms. It is a coincidence, I suppose, that the same object, modular curves, appears in both aspects. As a first example of modular curves, we introduce the j-line. 1 . Let S be a scheme over Q, and let E be an ellip­ tic curve over S. The j -invariant JE E f(S, 0) is a regular function satisfying the following condition. 2) . 2. Let S be any scheme over Q . 2) . (2) If two elliptic curves E and E' over S are isomorphic, then JE = )E1 .