Last edited by Zulusho
Friday, July 24, 2020 | History

7 edition of The theory of Jacobi forms found in the catalog.

The theory of Jacobi forms

by M. Eichler

  • 360 Want to read
  • 20 Currently reading

Published by Birkhäuser in Boston .
Written in English

    Subjects:
  • Jacobi forms.,
  • Forms, Modular.

  • Edition Notes

    Includes bibliography.

    StatementMartin Eichler, Don Zagier.
    SeriesProgress in mathematics ;, v. 55, Progress in mathematics (Boston, Mass.) ;, v. 55.
    ContributionsZagier, Don, 1951-
    Classifications
    LC ClassificationsQA243 .E36 1985
    The Physical Object
    Paginationv, 148 p. ;
    Number of Pages148
    ID Numbers
    Open LibraryOL2865163M
    ISBN 100817631801
    LC Control Number84028250

    The theory of Jacobi modular forms became an independent research subject after the famous book of Martin Eichler and Don Zagier “Jacobi modular forms” (Progress in Mathematics, vol. 55, ) which was cited more than a thousand times in research papers. This is due to many applications of Jacobi forms in arithmetic, topology, algebraic. Those who downloaded this book also downloaded the following books: Comments.

    Jacobi forms are holomorphic functions in two complex variables. They are modular in one variable and abelian (or double periodic) in another variable. The theory of Jacobi modular forms became an independent research subject after the famous book of Martin Eichler and Don Zagier “Jacobi modular forms” (Progress in Mathematics, vol. Modular forms and Jacobi forms play a central role in many areas of mathematics. Over the last 10–15 years, this theory has been extended to certain non-holomorphic functions, the so-called “harmonic Maass forms”. The first glimpses of this theory appeared in Ramanujan's enigmatic last letter to G. H. Hardy written from his deathbed.

    shall call \Jacobi forms of lattice index"). Motivation Seemingly complicated Jacobi forms are pullbacks of simple universal Jacobi forms of several variables (e.g. the m = 37 example and in nitely many others.) This yields a uni ed arithmetic theory for all kind of (elliptic) vector valued modular forms, namely: Theorem (S. ). coefficients of Siegel modular forms of genus two - but it is a relatively recent observation that the Jacobi forms have an arithmetic theory very analogous to the usual theory of modular forms: this began with Maass's proof of the Saito- Kurokawa conjecture [M] and was developed systematically in [E-Z].


Share this book
You might also like
Report of the directors of the Great Western Railway of Canada, for the half-year ending Jan. 31, 1857

Report of the directors of the Great Western Railway of Canada, for the half-year ending Jan. 31, 1857

Flame on high mountain and other stories.

Flame on high mountain and other stories.

Jade lore

Jade lore

Bless Me Father

Bless Me Father

Birmingham, Britains Olympic City.

Birmingham, Britains Olympic City.

Carolingian Portraits

Carolingian Portraits

Chemical discovery and invention in the twentieth century

Chemical discovery and invention in the twentieth century

Writing from the inner self

Writing from the inner self

The 2000 Import and Export Market for Inorganic Chemical Elements, Oxides and Halogen Salts in Jordan (World Trade Report)

The 2000 Import and Export Market for Inorganic Chemical Elements, Oxides and Halogen Salts in Jordan (World Trade Report)

Persian life and customs

Persian life and customs

Tachibana Moribe zenshu hokan

Tachibana Moribe zenshu hokan

The golden age; or, Future glory of North-America discovered by an angel to Celadon, in several entertaining visions.

The golden age; or, Future glory of North-America discovered by an angel to Celadon, in several entertaining visions.

Patterns of migration in Central Europe

Patterns of migration in Central Europe

Disadvantaged children

Disadvantaged children

The theory of Jacobi forms by M. Eichler Download PDF EPUB FB2

The Theory of Jacobi Forms (Progress in Mathematics (55)) th Edition. by Martin Eichler (Author), Don Zagier (Author) ISBN ISBN Cited by: Buy The Theory of Jacobi Forms (Progress in Mathematics) on FREE SHIPPING on qualified orders The Theory of Jacobi Forms (Progress in Mathematics): Eichler, Martin, Zagier, Don: : Books.

The Theory of Jacobi Forms. Authors (view affiliations) Martin Eichler; Don Zagier; Book. Citations; 3 Mentions; The Ring of Jacobi Forms. Martin Eichler, Don Zagier. About this book. Keywords. DEX Finite Natural cls computed tomography (CT) elliptic curve elliptic function form function functions holomorphic function modular form.

About this book. 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.

Additional Physical Format: Online version: Eichler, M. (Martin). Theory of Jacobi forms. Boston: Birkhäuser, (OCoLC) Material Type. The Theory of Jacobi Forms. Martin Eichler, Don Zagier. Springer Science & Business Media, - Mathematics - pages.

0 Reviews. The functions studied in this monogra9h are a. The functions studied in this monogra9h are a cross between elliptic functions and modular forms in one variable.

Specifically, we define a Jacobi form on SL (~) to be a holomorphic function 2 (JC = upper half-plane) satisfying the t\ transformation eouations 2Tiimcz* k CT +d a-r +b z) (1) ((cT+d) e cp(T,z) cp CT +d ' CT +d (2) rjl(T, z+h+]l) and having a Four*ier expansion of the form The Theory of Jacobi Forms by Martin Eichler,available at Book Depository with free delivery worldwide.

Try the new Google Books. View eBook. Get this book in print. ; Barnes&; Books-A-Million; IndieBound; Find in a library; All sellers» The Theory of Jacobi Forms. Martin Eichler, Don Zagier. Birkhäuser Boston, - Mathematics - pages. 0 Reviews. From inside the book. What people are saying - Write a review.

We haven. In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion, Lagrangian mechanics and Hamiltonian Hamilton–Jacobi equation is particularly useful in identifying conserved quantities for mechanical systems, which.

The theory of Jacobi forms. [M Eichler; Don Zagier] -- The functions studied in this monogra9h are a cross between elliptic functions and modular forms in one variable. Specifically, we define a Jacobi form on SL (~) to be a holomorphic function 2 (JC. In mathematics, a Jacobi form is an automorphic form on the Jacobi group, which is the semidirect product of the symplectic group Sp (n;R) and the Heisenberg group {\displaystyle H_ {R}^ { (n,h)}}.

The theory was first systematically studied by Eichler & Zagier (). Jacobi’s theorem:: r 4(n) = (8˙ 1(n); 4 - n 8˙ 1(n) 32˙ 1 n 4; 4 jn for all n2N = Z 1. Here ˙ 1(n) denotes the \sum of all divisors" function. Jacobi’s proof of his result leads already to the concept of theta-functions and modular forms by forming the generating function of r(n).

(We refer to x in. Chapter IV, which will be published as a separate work, goes more deeply into the Hecke theory of Jacobi forms.

In particular, it is shown with the aid of a trace formula that the equality of dimensions (9) actually comes from an isomorphism of the corresponding spaces as. y(τ,z) by Θ. y(τ,z) = X. x∈L. e((Q(x)τ +B(x,y)z)). Victoria de Quehen Jacobi Forms.

Motivation The main reference for this topic is The Theory of Jacobi Forms by Eichler and Zagier (). Their main interest in Jacobi forms was their relation to the Saito-Kurokawa lift. Siegel Modular Forms of Degree Two.

This volume is thus a complement to the seminal book on Jacobi forms by M. Eichler and D. Zagier. Incorporating results of the authors' original research, this exposition is meant for researchers and graduate students interested in algebraic groups and number theory, in particular, modular and automorphic forms.

This book introduces the reader to the fascinating world of modular forms through a problem-solving approach. As such, besides researchers, the book can be used by the undergraduate and graduate students for self-instruction. Download online ebook. Advances in Computer Graphics and Computer Vision: International Conferences VISAPP and GRAPPSetúbal, Portugal, February, Revised Selected in Computer and Information Science).

The Theory of Jacobi Forms (Progress in Mathematics) The Autobiography of Emperor Haile Sellassie I: King of Kings of All Ethiopia and Lord of All Lords (My Life and Ethiopia's Progress) (My Life and.

Abstract. This book is intended to serve both as an introduction and a reference to spectral and inverse spectral theory of Jacobi operators (i.e., second order symmetric di erence operators) and applications of these theories to the Toda and Kac-van Moerbeke hierarchy.

Starting from second order di erence equations we move on to self-adjoint. The theory of Jacobi modular forms became an independent research subject after the famous book of Martin Eichler and Don Zagier “Jacobi modular forms” (Progress in Mathematics, vol.

55, ) which was cited more than a thousand times in research papers.A very nice and systematic development of the theory of holo- morphic Jacobi forms is given in the book by Eichler and Zagier. In addition to the Communicated by U. Kühn. A. Pitale () Department of Mathematics, University of Oklahoma, Norman, OKUSA e .Hecke–Jacobi cusp eigenforms of weight k > 4 and k≡ 0 mod 4 can written explicitly as a linear combination of theta series.

Finally the basis problem of Jacobi forms of square-free index is.