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Jacobi-Like Forms, Pseudodifferential Operators, and Quasimodular Forms

2019-11-20 Mathematics
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Release : 2019-11-20
Genre : Mathematics
Kind : eBook
Book Rating : 235/5 ( reviews)

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Book Synopsis Jacobi-Like Forms, Pseudodifferential Operators, and Quasimodular Forms by : YoungJu Choie

Download or read book Jacobi-Like Forms, Pseudodifferential Operators, and Quasimodular Forms written by YoungJu Choie. This book was released on 2019-11-20. Available in PDF, EPUB and Kindle. Book excerpt: This book explores various properties of quasimodular forms, especially their connections with Jacobi-like forms and automorphic pseudodifferential operators. The material that is essential to the subject is presented in sufficient detail, including necessary background on pseudodifferential operators, Lie algebras, etc., to make it accessible also to non-specialists. The book also covers a sufficiently broad range of illustrations of how the main themes of the book have occurred in various parts of mathematics to make it attractive to a wider audience. The book is intended for researchers and graduate students in number theory.

The 1-2-3 of Modular Forms

2008-02-10 Mathematics
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Release : 2008-02-10
Genre : Mathematics
Kind : eBook
Book Rating : 194/5 ( reviews)

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Book Synopsis The 1-2-3 of Modular Forms by : Jan Hendrik Bruinier

Download or read book The 1-2-3 of Modular Forms written by Jan Hendrik Bruinier. This book was released on 2008-02-10. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Theory of Jacobi Forms

2013-12-14 Mathematics
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Release : 2013-12-14
Genre : Mathematics
Kind : eBook
Book Rating : 628/5 ( reviews)

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Book Synopsis The Theory of Jacobi Forms by : Martin Eichler

Download or read book The Theory of Jacobi Forms written by Martin Eichler. This book was released on 2013-12-14. Available in PDF, EPUB and Kindle. Book excerpt: 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\-10 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 00 e2Tii(nT +rz) (3) cp(T, z) 2: c(n, r) 2:: rE~ n=O 2 r ~ 4nm Here k and m are natural numbers, called the weight and index of rp, respectively. Note that th e function cp (T, 0) is an ordinary modular formofweight k, whileforfixed T thefunction z-+rjl( -r, z) isa function of the type normally used to embed the elliptic curve ~/~T + ~ into a projective space. If m= 0, then cp is independent of z and the definition reduces to the usual notion of modular forms in one variable. We give three other examples of situations where functions satisfying (1)-(3) arise classically: 1. Theta series. Let Q: ~-+ ~ be a positive definite integer valued quadratic form and B the associated bilinear form.

Acta Arithmetica

2009 Mathematics
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Release : 2009
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Acta Arithmetica by :

Download or read book Acta Arithmetica written by . This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt:

Pseudodifferential Operators with Automorphic Symbols

2015-06-22 Mathematics
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Release : 2015-06-22
Genre : Mathematics
Kind : eBook
Book Rating : 574/5 ( reviews)

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Book Synopsis Pseudodifferential Operators with Automorphic Symbols by : André Unterberger

Download or read book Pseudodifferential Operators with Automorphic Symbols written by André Unterberger. This book was released on 2015-06-22. Available in PDF, EPUB and Kindle. Book excerpt: The main results of this book combine pseudo differential analysis with modular form theory. The methods rely for the most part on explicit spectral theory and the extended use of special functions. The starting point is a notion of modular distribution in the plane, which will be new to most readers and relates under the Radon transformation to the classical one of modular form of the non-holomorphic type. Modular forms of the holomorphic type are addressed too in a more concise way, within a general scheme dealing with quantization theory and elementary, but novel, representation-theoretic concepts.

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