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The Gross-Zagier Formula on Shimura Curves

This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on;

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The Gross-Zagier Formula on Shimura Curves

This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on;

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Arithmetic and Geometry

elliptic curves with the height of Heegner points on the curves. Zhang, X. Yuan, and Wei Zhang prove the Gross-Zagier formula on Shimura curves and;

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Arithmetic and Geometry

elliptic curves with the height of Heegner points on the curves. Zhang, X. Yuan, and Wei Zhang prove the Gross-Zagier formula on Shimura curves and;

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Heegner Points and Rankin L-Series

The seminal formula of Gross and Zagier relating heights of Heegner points to derivatives of the associated Rankin L-series has led to many;

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Heegner Points and Rankin L-Series

The seminal formula of Gross and Zagier relating heights of Heegner points to derivatives of the associated Rankin L-series has led to many;

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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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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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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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Galois Representations in Arithmetic Algebraic Geometry

attention, e.g. Erez on geometric trends in Galois module theory; Mazur on rational points on curves and varieties; Moonen on Shimura varieties;

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Arithmetic Compactifications of PEL-Type Shimura Varieties

of all PEL-type Shimura varieties, providing the logical foundation for several exciting recent developments. The book is designed to be;

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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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On Certain L-Functions

formula and its consequences, the Gross-Prasad conjecture, and more. The volume also includes an expository article on Shahidi's contributions to;

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A Local Relative Trace Formula for the Ginzburg-Rallis Model

is able to prove the geometric side of a local relative trace formula for the Ginzburg-Rallis model. Then by applying such formula, the author;

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Shimura Varieties

This is the second volume of a series of mainly expository articles on the arithmetic theory of automorphic forms. It forms a sequel to On;

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Elliptic Functions

invariants. Part three covers curves with non-integral invariants, and applies the Tate parametrization to give Serre's results on division points;

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Collected Papers V: 2002-2012

In 1996 the AMS awarded Goro Shimura the Steele Prize for Lifetime Achievement: To Goro Shimura for his important and extensive work on;

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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 Tales

understand this captivating problem. The key to the conjecture lies in elliptic curves, which may appear simple, but arise from some very deep--and;

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Elliptic Tales

understand this captivating problem. The key to the conjecture lies in elliptic curves, which may appear simple, but arise from some very deep--and;

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Advanced Topics in the Arithmetic of Elliptic Curves

In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that the theory;

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Cambridge Studies in Advanced Mathematics Cohomology of Drinfeld Modular Varieties

for function fields. These varieties are the analogues for function fields of the Shimura varieties over number fields. The Langlands;

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Cambridge Studies in Advanced Mathematics Cohomology of Drinfeld Modular Varieties

for function fields. These varieties are the analogues for function fields of the Shimura varieties over number fields. The Langlands;

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Elliptic Curves and Big Galois Representations

curves, in particular the Birch and Swinnerton-Dyer (BSD) formula. Three main steps are outlined: the first is to parametrise 'big' cohomology;

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Bernoulli Numbers and Zeta Functions

. This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the;

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Automorphic Forms & Galois Representati

in volume two include curves and vector bundles in p-adic Hodge theory, associators, Shimura varieties, the birational section conjecture, and other;

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Statistics At Square One 11th

chapter are strengthened by the addition of new sections on reading and reporting statistics and formula appreciation.;

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