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Modular Forms and Special Cycles on Shimura Curves. (AM-161)

Modular Forms and Special Cycles on Shimura Curves is a thorough study of the generating functions constructed from special cycles, both;

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Elliptic Curves. (MN-40), Volume 40

forms--come together in Eichler-Shimura theory, which constructs elliptic curves out of modular forms of a special kind. The converse, that all;

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Intersections of Hirzebruch-Zagier Divisors and CM Cycles

information about the Arakelov intersection theory of special cycles on Shimura varieties of orthogonal and unitary type. Here, the Eisenstein series;

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Arithmetic Compactifications of PEL-Type Shimura Varieties

generalizations of modular curves, are useful for studying the arithmetic properties of automorphic forms and automorphic representations, and they have;

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Introduction to Arithmetic Theory of Automorphic Functions

ubiquitous in number theory. This book introduces the reader to the subject and in particular to elliptic modular forms with emphasis on their number;

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Non-Archimedean L-Functions and Arithmetical Siegel Modular Forms

are L-functions of classical Siegel modular forms whose special values are studied using the Rankin-Selberg method and the action of certain;

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The Gross-Zagier Formula on Shimura Curves

formulas. The Gross-Zagier Formula on Shimura Curves will be of great use to students wishing to enter this area and to those already working in it.;

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The Gross-Zagier Formula on Shimura Curves

formulas. The Gross-Zagier Formula on Shimura Curves will be of great use to students wishing to enter this area and to those already working in it.;

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Elliptic Curves, Modular Forms and Iwasawa Theory

collection of contributions covers a range of topics in number theory, concentrating on the arithmetic of elliptic curves, modular forms, and Galois;

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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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Computational Aspects of Modular Forms and Galois Representations

Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and;

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Modular Forms

This book is a translation of the earlier book written by Koji Doi and the author, who revised it substantially for this English edition;

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Hilbert Modular Forms

Important results on the Hilbert modular group and Hilbert modular forms are introduced and described in this book. In recent times, this;

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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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Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108

This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study;

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Jacobi Forms Finite Quadratic Modules and Weil Representations over Number Fiel

arithmetic theory of Hilbert modular forms, its L-series, and into elliptic curves over number fields. This work is inspired by the classical theory;

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Harmonic Maass Forms and Mock Modular Forms

and mock modular forms, together with a wide variety of applications to algebraic number theory, combinatorics, elliptic curves, mathematical;

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Modular Forms and Functions

This book provides an introduction to the theory of elliptic modular functions and forms, a subject of increasing interest because of its;

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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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p-Adic Automorphic Forms on Shimura Varieties

holomorphic automorphic forms on Shimura varieties and also for more general (nonholomorphic) cohomological automorphic forms on automorphic manifolds;

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Elliptic Curves, Modular Forms and Their L-functions

of elliptic curves, modular forms, and $L$-functions. His main goal is to provide the reader with the big picture of the surprising connections among;

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Elliptic Curves, Hilbert Modular Forms And Galois Deformatio

. The notes by Mladen Dimitrov present the basics of the arithmetic theory of Hilbert modular forms and varieties, with an emphasis on the study;

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Cambridge Studies in Advanced Mathematics Cohomology of Drinfeld Modular Varieties

Cohomology of Drinfeld Modular Varieties provides an introduction, in two volumes, both to this subject and to the Langlands correspondence;

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Cambridge Studies in Advanced Mathematics Cohomology of Drinfeld Modular Varieties

Cohomology of Drinfeld Modular Varieties provides an introduction, in two volumes, both to this subject and to the Langlands correspondence;

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O Minimality & Diophantine Geometry

of the Andre-Oort conjecture for products of modular curves. The basic strategy has three main ingredients: the Pila-Wilkie theorem, bounds on;

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Elliptic Curves and Big Galois Representations

The arithmetic properties of modular forms and elliptic curves lie at the heart of modern number theory. This book develops a;

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The Map of My Life

Lifetime Achievement from the American Mathematical Society. He is the author of Elementary Dirichlet Series and Modular Forms (Springer 2007;

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