Used
/
Quantity Available: 0

We're sorry; this specific copy is no longer available. AbeBooks has millions of books. We've listed similar copies below.

The Gross-Zagier Formula on Shimura Curves (Annals of Mathematics Studies). Bookseller Inventory #

**Synopsis:**

This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations.

The book begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations with rational coefficients attached naturally to abelian varieties parametrized by Shimura curves. This is followed by a complete proof of its coherent analogue: the Waldspurger formula, which relates the periods of integrals and the special values of L-series by means of Weil representations. The Gross-Zagier formula is then reformulated in terms of incoherent Weil representations and Kudla's generating series. Using Arakelov theory and the modularity of Kudla's generating series, the proof of the Gross-Zagier formula is reduced to local 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.

**About the Author:**
**Xinyi Yuan** is assistant professor of mathematics at Princeton University. **Shou-wu Zhang** is professor of mathematics at Princeton University and Columbia University. **Wei Zhang** is assistant professor of mathematics at Columbia University.

Title: **The Gross-Zagier Formula on Shimura Curves (...**

Book Condition: **Good**

Published by
Princeton University Press
(2013)

ISBN 10: 0691155925
ISBN 13: 9780691155920

New
Quantity Available: 3

Seller

Rating

**Book Description **Princeton University Press, 2013. PAP. Book Condition: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Bookseller Inventory # WP-9780691155920

More Information About This Seller | Ask Bookseller a Question

Published by
Princeton University Press
(2012)

ISBN 10: 0691155925
ISBN 13: 9780691155920

New
Paperback
Quantity Available: 1

Seller

Rating

**Book Description **Princeton University Press, 2012. Paperback. Book Condition: New. book. Bookseller Inventory # M0691155925

More Information About This Seller | Ask Bookseller a Question

Published by
Princeton University Press, United States
(2012)

ISBN 10: 0691155925
ISBN 13: 9780691155920

New
Paperback
Quantity Available: 1

Seller

Rating

**Book Description **Princeton University Press, United States, 2012. Paperback. Book Condition: New. Language: English . Brand New Book. This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations. The book begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations with rational coefficients attached naturally to abelian varieties parametrized by Shimura curves. This is followed by a complete proof of its coherent analogue: the Waldspurger formula, which relates the periods of integrals and the special values of L-series by means of Weil representations. The Gross-Zagier formula is then reformulated in terms of incoherent Weil representations and Kudla s generating series. Using Arakelov theory and the modularity of Kudla s generating series, the proof of the Gross-Zagier formula is reduced to local 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. Bookseller Inventory # AAH9780691155920

More Information About This Seller | Ask Bookseller a Question

Published by
Princeton University Press, United States
(2012)

ISBN 10: 0691155925
ISBN 13: 9780691155920

New
Paperback
Quantity Available: 1

Seller

Rating

**Book Description **Princeton University Press, United States, 2012. Paperback. Book Condition: New. Language: English . Brand New Book. This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations. The book begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations with rational coefficients attached naturally to abelian varieties parametrized by Shimura curves. This is followed by a complete proof of its coherent analogue: the Waldspurger formula, which relates the periods of integrals and the special values of L-series by means of Weil representations. The Gross-Zagier formula is then reformulated in terms of incoherent Weil representations and Kudla s generating series. Using Arakelov theory and the modularity of Kudla s generating series, the proof of the Gross-Zagier formula is reduced to local 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. Bookseller Inventory # AAH9780691155920

More Information About This Seller | Ask Bookseller a Question

Published by
Princeton University Press
(2013)

ISBN 10: 0691155925
ISBN 13: 9780691155920

New
Quantity Available: > 20

Seller

Rating

**Book Description **Princeton University Press, 2013. PAP. Book Condition: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Bookseller Inventory # IQ-9780691155920

More Information About This Seller | Ask Bookseller a Question

Published by
Princeton University Press
(2013)

ISBN 10: 0691155925
ISBN 13: 9780691155920

New
Quantity Available: > 20

Seller

Rating

**Book Description **Princeton University Press, 2013. PAP. Book Condition: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Bookseller Inventory # IQ-9780691155920

More Information About This Seller | Ask Bookseller a Question

Published by
Princeton University Press

ISBN 10: 0691155925
ISBN 13: 9780691155920

New
Paperback
Quantity Available: 3

Seller

Rating

**Book Description **Princeton University Press. Paperback. Book Condition: new. BRAND NEW, The Gross-Zagier Formula on Shimura Curves, Xinyi Yuan, Shou-Wu Zhang, Wei Zhang, This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations. The book begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations with rational coefficients attached naturally to abelian varieties parametrized by Shimura curves. This is followed by a complete proof of its coherent analogue: the Waldspurger formula, which relates the periods of integrals and the special values of L-series by means of Weil representations. The Gross-Zagier formula is then reformulated in terms of incoherent Weil representations and Kudla's generating series. Using Arakelov theory and the modularity of Kudla's generating series, the proof of the Gross-Zagier formula is reduced to local 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. Bookseller Inventory # B9780691155920

More Information About This Seller | Ask Bookseller a Question

Published by
Princeton University Press
(2017)

ISBN 10: 0691155925
ISBN 13: 9780691155920

Used
Paperback
Quantity Available: 2

Seller

Rating

**Book Description **Princeton University Press, 2017. Paperback. Book Condition: Very Good. Great condition with minimal wear, aging, or shelf wear. This item is printed on demand. Bookseller Inventory # P020691155925

More Information About This Seller | Ask Bookseller a Question

Published by
Princeton University Press
(2017)

ISBN 10: 0691155925
ISBN 13: 9780691155920

New
Paperback
Quantity Available: 2

Seller

Rating

**Book Description **Princeton University Press, 2017. Paperback. Book Condition: New. Never used! This item is printed on demand. Bookseller Inventory # P110691155925

More Information About This Seller | Ask Bookseller a Question

Published by
Princeton University Press
(2017)

ISBN 10: 0691155925
ISBN 13: 9780691155920

Used
Paperback
Quantity Available: 2

Seller

Rating

**Book Description **Princeton University Press, 2017. Paperback. Book Condition: Like New. Almost new condition. This item is printed on demand. Bookseller Inventory # P010691155925

More Information About This Seller | Ask Bookseller a Question