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Abelian Varieties with Complex Multiplication and Modular Functions

modular functions, and is called complex multiplication of such functions. In 1900 Hilbert proposed the generalization of these as the twelfth;

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Introduction to Arithmetic Theory of Automorphic Functions

associate zeta functions to modular forms. At a more advanced level, complex multiplication of elliptic curves and abelian varieties is discussed;

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Complex Multiplication and Lifting Problems

Abelian varieties with complex multiplication lie at the origins of class field theory, and they play a central role in the contemporary;

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Topics In Complex Function Theory

theory, continues with automorphic functions and the theory of abelian integrals and ends with the theory of abelian functions and modular;

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Arithmetic Compactifications of PEL-Type Shimura Varieties

defining and representing moduli problems of abelian schemes with PEL structures * An analysis of the degeneration of abelian varieties with PEL;

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Complex Tori and Abelian Varieties

This graduate-level textbook introduces the classical theory of complex tori and abelian varieties, while presenting in parallel more;

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Complex Multiplication

This is a self-contained 2010 account of the state of the art in classical complex multiplication that includes recent results on rings;

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Abelian Varieties

results about abelian varieties. It includes expositions of analytic methods applicable over the ground field of complex numbers, as well as;

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Intersections of Hirzebruch-Zagier Divisors and CM Cycles

special cycles are complex multiplication points and the Hirzebruch-Zagier divisors. By developing new techniques in deformation theory, the;

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Number Theory Related to Modular Curves

of Galois representations attached to modular forms, rational points on elliptic and modular curves, modularity of some families of Abelian;

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Methods of the Theory of Generalized Functions

Poisson integral transforms and operational calculus, with the traditional material augmented by the theory of Fourier series, abelian theorems;

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Methods of the Theory of Generalized Functions

Poisson integral transforms and operational calculus, with the traditional material augmented by the theory of Fourier series, abelian theorems;

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London Mathematical Society Lecture Note Series

of one complex variable. When an abelian manifold is embedded in a projective space it is termed an abelian variety in an algebraic geometrical;

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Toric Varieties in Several Complex Variables

The present book deals with integral representations for holomorphic functions of several complex variables and holomorphic extensions;

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Advanced Topics in the Arithmetic of Elliptic Curves

modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira;

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Modular Forms on Schiermonnikoog

Modular forms are functions with an enormous amount of symmetry that play a central role in number theory, connecting it with analysis and;

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O Minimality & Diophantine Geometry

and model theoretic aspects of the subject. These include Martin Orr's survey of abelian varieties, Christopher Daw's introduction to Shimura;

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Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design

non Abelian groups. A solid foundation of this complex topic is provided by beginning with a review of signals and their mathematical models;

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Compactifying Moduli Spaces for Abelian Varieties

the theory to higher degree polarizations and discuss various applications to moduli spaces for abelian varieties with level structure.;

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Representations of Elementary Abelian P -groups and Vector Bundles

Questions about modular representation theory of finite groups can often be reduced to elementary abelian subgroups. This is the first book;

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Algebraic And Arithmetic Structures Of Moduli Spaces (Sapporo 2007)

of complex vector bundles, moduli of abelian varieties and theory of display, moduli of Fermat varieties and some topics on cubic threefolds. Among;

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Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces

surfaces, group actions on surfaces and topological properties of moduli spaces of complex curves and Abelian varieties.;

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Fourier Analysis on Finite Abelian Groups

application of the [discrete] Fourier transform to finite Abelian groups. With countless examples and unique exercise sets at the end of each section;

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Geometry, Algebra, Number Theory, and Their Information Technology Applications

-functions Arithmetic geometry, with special emphasis on algebraic cycles, Shimura varieties, and explicit methods in the theory of abelian varieties;

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Elements of the Representation Theory of the Jacobi Group

embeddings of certain algebraic varieties and homogeneous spaces * correspondences between di?erent kinds of modular forms * L-functions associated;

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Stochastic Processes

Function Theory Volume II - Automorphic and Abelian Integrals C. L. Siegel Topics in Complex Function Theory, Volume III - Abelian Functions;

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Diophantine Approximation and Abelian Varieties

varieties , Ann. Math.133 (1991) and together give an approach to the proof that is accessible to Ph.D-level students in number theory and;

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