Download E-books Abelian Varieties with Complex Multiplication and Modular Functions PDF

Reciprocity legislation of assorted varieties play a relevant position in quantity concept. within the simplest case, one obtains a clear formula through roots of team spirit, that are unique values of exponential features. an identical concept may be constructed for certain values of elliptic or elliptic modular features, and is termed advanced multiplication of such features. In 1900 Hilbert proposed the generalization of those because the 12th of his recognized difficulties. during this e-book, Goro Shimura presents the main finished generalizations of this sort through mentioning a number of reciprocity legislation by way of abelian kinds, theta capabilities, and modular features of a number of variables, together with Siegel modular functions.

This topic is heavily attached with the zeta functionality of an abelian sort, that's additionally lined as a major subject matter within the e-book. The 3rd subject explored by means of Shimura is many of the algebraic kin one of the sessions of abelian integrals. The research of such algebraicity is comparatively new, yet has attracted the curiosity of more and more many researchers. some of the issues mentioned during this publication haven't been lined ahead of. specifically, this can be the 1st e-book within which the subjects of assorted algebraic family one of the classes of abelian integrals, in addition to the targeted values of theta and Siegel modular features, are taken care of extensively.

Show description

Read Online or Download Abelian Varieties with Complex Multiplication and Modular Functions PDF

Similar Algebraic Geometry books

The Unreal Life of Oscar Zariski

The 1st biography of Oscar Zariski - arguably one of many maximum mathematicians of the 20 th century. established mostly on interviews with Zariski, his relations, and his colleagues, it incorporates a precis of a few of his pioneering paintings in addition to his own background which spans approximately eighty years and covers many of the globe.

Using Algebraic Geometry (Graduate Texts in Mathematics)

The invention of recent algorithms for facing polynomial equations, and their implementation on quickly, reasonably cheap pcs, has revolutionized algebraic geometry and ended in interesting new functions within the box. This publication info many makes use of of algebraic geometry and highlights fresh functions of Grobner bases and resultants.

Basic Algebraic Geometry 2: Schemes and Complex Manifolds

Quantity 2: Schemes and complicated Manifolds, covers generalizations in varied instructions of the affine and projective forms that shape the cloth for the 1st quantity. Discusses the origins of algebraic geometry. Paper. DLC: Geometry - Algebraic.

Additional resources for Abelian Varieties with Complex Multiplication and Modular Functions

Show sample text content

Rated 4.94 of 5 – based on 15 votes