Jacobi Forms Finite Quadratic Modules And Weil Representations Over Number Fields
Download Jacobi Forms Finite Quadratic Modules And Weil Representations Over Number Fields full books in PDF, epub, and Kindle. Read online free Jacobi Forms Finite Quadratic Modules And Weil Representations Over Number Fields ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Jacobi Forms Finite Quadratic Modules and Weil Representations over Number Fields
Author | : Hatice Boylan |
Publsiher | : Springer |
Total Pages | : 150 |
Release | : 2014-12-05 |
Genre | : Mathematics |
ISBN | : 9783319129167 |
Download Jacobi Forms Finite Quadratic Modules and Weil Representations over Number Fields Book in PDF, Epub and Kindle
The new theory of Jacobi forms over totally real number fields introduced in this monograph is expected to give further insight into the arithmetic theory of Hilbert modular forms, its L-series, and into elliptic curves over number fields. This work is inspired by the classical theory of Jacobi forms over the rational numbers, which is an indispensable tool in the arithmetic theory of elliptic modular forms, elliptic curves, and in many other disciplines in mathematics and physics. Jacobi forms can be viewed as vector valued modular forms which take values in so-called Weil representations. Accordingly, the first two chapters develop the theory of finite quadratic modules and associated Weil representations over number fields. This part might also be interesting for those who are merely interested in the representation theory of Hilbert modular groups. One of the main applications is the complete classification of Jacobi forms of singular weight over an arbitrary totally real number field.
L Functions and Automorphic Forms
Author | : Jan Hendrik Bruinier,Winfried Kohnen |
Publsiher | : Springer |
Total Pages | : 366 |
Release | : 2018-02-22 |
Genre | : Mathematics |
ISBN | : 9783319697123 |
Download L Functions and Automorphic Forms Book in PDF, Epub and Kindle
This book presents a collection of carefully refereed research articles and lecture notes stemming from the Conference "Automorphic Forms and L-Functions", held at the University of Heidelberg in 2016. The theory of automorphic forms and their associated L-functions is one of the central research areas in modern number theory, linking number theory, arithmetic geometry, representation theory, and complex analysis in many profound ways. The 19 papers cover a wide range of topics within the scope of the conference, including automorphic L-functions and their special values, p-adic modular forms, Eisenstein series, Borcherds products, automorphic periods, and many more.
Elliptic Curves Hilbert Modular Forms and Galois Deformations
Author | : Laurent Berger,Gebhard Böckle,Lassina Dembélé,Mladen Dimitrov,Tim Dokchitser,John Voight |
Publsiher | : Springer Science & Business Media |
Total Pages | : 257 |
Release | : 2013-06-13 |
Genre | : Mathematics |
ISBN | : 9783034806183 |
Download Elliptic Curves Hilbert Modular Forms and Galois Deformations Book in PDF, Epub and Kindle
The notes in this volume correspond to advanced courses held at the Centre de Recerca Matemàtica as part of the research program in Arithmetic Geometry in the 2009-2010 academic year. The notes by Laurent Berger provide an introduction to p-adic Galois representations and Fontaine rings, which are especially useful for describing many local deformation rings at p that arise naturally in Galois deformation theory. The notes by Gebhard Böckle offer a comprehensive course on Galois deformation theory, starting from the foundational results of Mazur and discussing in detail the theory of pseudo-representations and their deformations, local deformations at places l ≠ p and local deformations at p which are flat. In the last section,the results of Böckle and Kisin on presentations of global deformation rings over local ones are discussed. The notes by Mladen Dimitrov present the basics of the arithmetic theory of Hilbert modular forms and varieties, with an emphasis on the study of the images of the attached Galois representations, on modularity lifting theorems over totally real number fields, and on the cohomology of Hilbert modular varieties with integral coefficients. The notes by Lassina Dembélé and John Voight describe methods for performing explicit computations in spaces of Hilbert modular forms. These methods depend on the Jacquet-Langlands correspondence and on computations in spaces of quaternionic modular forms, both for the case of definite and indefinite quaternion algebras. Several examples are given, and applications to modularity of Galois representations are discussed. The notes by Tim Dokchitser describe the proof, obtained by the author in a joint project with Vladimir Dokchitser, of the parity conjecture for elliptic curves over number fields under the assumption of finiteness of the Tate-Shafarevich group. The statement of the Birch and Swinnerton-Dyer conjecture is included, as well as a detailed study of local and global root numbers of elliptic curves and their classification.
Rational Points on Modular Elliptic Curves
Author | : Henri Darmon |
Publsiher | : American Mathematical Soc. |
Total Pages | : 148 |
Release | : 2024 |
Genre | : Mathematics |
ISBN | : 0821889451 |
Download Rational Points on Modular Elliptic Curves Book in PDF, Epub and Kindle
The book surveys some recent developments in the arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely related issues. The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, complex multiplication and the Heegner point construction. The next three chapters introduce variants of modular parametrizations in which modular curves are replaced by Shimura curves attached to certain indefinite quaternion algebras. The main new contributions are found in Chapters 7-9, which survey the author's attempts to extend the theory of Heegner points and complex multiplication to situations where the base field is not a CM field. Chapter 10 explains the proof of Kolyvagin's theorem, which relates Heegner points to the arithmetic of elliptic curves and leads to the best evidence so far for the Birch and Swinnerton-Dyer conjecture.
Mathematical Reviews
Author | : Anonim |
Publsiher | : Unknown |
Total Pages | : 1852 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : UVA:X006195257 |
Download Mathematical Reviews Book in PDF, Epub and Kindle
Reviews in Number Theory 1984 96
Author | : Anonim |
Publsiher | : Unknown |
Total Pages | : 1032 |
Release | : 1997 |
Genre | : Number theory |
ISBN | : UCAL:B5102243 |
Download Reviews in Number Theory 1984 96 Book in PDF, Epub and Kindle
The 1 2 3 of Modular Forms
Author | : Jan Hendrik Bruinier,Gerard van der Geer,Günter Harder,Don Zagier |
Publsiher | : Springer Science & Business Media |
Total Pages | : 273 |
Release | : 2008-02-10 |
Genre | : Mathematics |
ISBN | : 9783540741190 |
Download The 1 2 3 of Modular Forms Book in PDF, Epub and Kindle
This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.
Elliptic Curves
Author | : Henry McKean,Victor Moll |
Publsiher | : Cambridge University Press |
Total Pages | : 300 |
Release | : 1999-08-13 |
Genre | : Mathematics |
ISBN | : 0521658179 |
Download Elliptic Curves Book in PDF, Epub and Kindle
An introductory 1997 account in the style of the original discoverers, treating the fundamental themes even-handedly.