Heegner Points And Derivatives Of L Series
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Author | : Henri Darmon |
Publisher | : Cambridge University Press |
Total Pages | : 386 |
Release | : 2004-06-21 |
Genre | : Mathematics |
ISBN | : 9780521836593 |
Thirteen articles by leading contributors on the history of the Gross-Zagier formula and its developments.
Author | : Benedict H. Gross |
Publisher | : |
Total Pages | : 89 |
Release | : 1987 |
Genre | : |
ISBN | : |
Author | : B. H. Gross |
Publisher | : |
Total Pages | : 150 |
Release | : 1985 |
Genre | : |
ISBN | : |
Author | : Henri Darmon |
Publisher | : |
Total Pages | : 367 |
Release | : 2004 |
Genre | : Curves, Elliptic |
ISBN | : 9780511215476 |
Author | : Xinyi Yuan |
Publisher | : Princeton University Press |
Total Pages | : 266 |
Release | : 2013 |
Genre | : Mathematics |
ISBN | : 0691155925 |
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.
Author | : Luis Dieulefait |
Publisher | : Cambridge University Press |
Total Pages | : 539 |
Release | : 2015-10-08 |
Genre | : Mathematics |
ISBN | : 1316381447 |
The 'Arithmetic and Geometry' trimester, held at the Hausdorff Research Institute for Mathematics in Bonn, focussed on recent work on Serre's conjecture and on rational points on algebraic varieties. The resulting proceedings volume provides a modern overview of the subject for graduate students in arithmetic geometry and Diophantine geometry. It is also essential reading for any researcher wishing to keep abreast of the latest developments in the field. Highlights include Tim Browning's survey on applications of the circle method to rational points on algebraic varieties and Per Salberger's chapter on rational points on cubic hypersurfaces.
Author | : Ze-Li Dou |
Publisher | : Springer Science & Business Media |
Total Pages | : 131 |
Release | : 2012-12-15 |
Genre | : Mathematics |
ISBN | : 3642287085 |
"Six Short Chapters on Automorphic Forms and L-functions" treats the period conjectures of Shimura and the moment conjecture. These conjectures are of central importance in contemporary number theory, but have hitherto remained little discussed in expository form. The book is divided into six short and relatively independent chapters, each with its own theme, and presents a motivated and lively account of the main topics, providing professionals an overall view of the conjectures and providing researchers intending to specialize in the area a guide to the relevant literature. Ze-Li Dou and Qiao Zhang are both associate professors of Mathematics at Texas Christian University, USA.
Author | : J. B. Friedlander |
Publisher | : Springer Science & Business Media |
Total Pages | : 224 |
Release | : 2006 |
Genre | : |
ISBN | : 3540363637 |
Author | : Steven D. Galbraith |
Publisher | : Springer Science & Business Media |
Total Pages | : 386 |
Release | : 2008-08-25 |
Genre | : Computers |
ISBN | : 3540855033 |
This book constitutes the thoroughly refereed proceedings of the Second International Conference on Pairing-Based Cryptography, Pairing 2008, held in London, UK, in September 2008. The 20 full papers, presented together with the contributions resulting from 3 invited talks, were carefully reviewed and selected from 50 submissions. The contents are organized in topical sections on cryptography, mathematics, constructing pairing-friendly curves, implementation of pairings, and hardware implementation.
Author | : Ellen E. Eischen |
Publisher | : Springer |
Total Pages | : 351 |
Release | : 2016-09-26 |
Genre | : Mathematics |
ISBN | : 3319309765 |
Exploring the interplay between deep theory and intricate computation, this volume is a compilation of research and survey papers in number theory, written by members of the Women In Numbers (WIN) network, principally by the collaborative research groups formed at Women In Numbers 3, a conference at the Banff International Research Station in Banff, Alberta, on April 21-25, 2014. The papers span a wide range of research areas: arithmetic geometry; analytic number theory; algebraic number theory; and applications to coding and cryptography. The WIN conference series began in 2008, with the aim of strengthening the research careers of female number theorists. The series introduced a novel research-mentorship model: women at all career stages, from graduate students to senior members of the community, joined forces to work in focused research groups on cutting-edge projects designed and led by experienced researchers. The goals for Women In Numbers 3 were to establish ambitious new collaborations between women in number theory, to train junior participants about topics of current importance, and to continue to build a vibrant community of women in number theory. Forty-two women attended the WIN3 workshop, including 15 senior and mid-level faculty, 15 junior faculty and postdocs, and 12 graduate students.