Quantization and Non-holomorphic Modular Forms by Andre Unterberger

Cover of: Quantization and Non-holomorphic Modular Forms | Andre Unterberger

Published by Springer .

Written in English

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Subjects:

  • Differential equations,
  • Integral equations,
  • Number Theory,
  • Mathematics,
  • Analytic Mechanics (Mathematical Aspects),
  • Science,
  • Science/Mathematics,
  • General,
  • 11F03,
  • 11L05,
  • 35S99,
  • 44A12,
  • 81S99,
  • Kloosterman series,
  • Lax-Phillips theory,
  • Mathematics / Number Theory,
  • Medical-General,
  • Non-holomorphic modular forms,
  • Advanced,
  • Quantum Theory,
  • Forms, Modular,
  • Geometric quantization

Edition Notes

Lecture Notes in Mathematics

Book details

The Physical Object
FormatPaperback
Number of Pages253
ID Numbers
Open LibraryOL9063458M
ISBN 103540678611
ISBN 109783540678618

Download Quantization and Non-holomorphic Modular Forms

This is a new approach to the theory of non-holomorphic modular forms, based on ideas from quantization theory or pseudodifferential analysis. Extending the Rankin-Selberg method so as to apply it to the calculation of the Roelcke-Selberg decomposition of the product of two Eisenstein series, one lets Maass cusp-forms appear as residues of.

This is a new approach to the theory of non-holomorphic modular forms, based on ideas from quantization theory or pseudodifferential analysis.

Extending the Rankin-Selberg method so as to apply it to the calculation of the Roelcke-Selberg decomposition of the product of two Eisenstein series, oneBrand: Springer-Verlag Berlin Heidelberg.

Get this from a library. Quantization and non-holomorphic modular forms. [André Unterberger] -- This is a new approach to the theory of non-holomorphic modular forms, based on ideas from quantization theory or pseudodifferential analysis.

Extending the Rankin-Selberg method so as to apply it to. This is a new approach to the theory of non-holomorphic modular forms, based on ideas from quantization theory or pseudodifferential analysis.

Rating: (not yet rated) 0 with reviews - Be the first. Cite this chapter as: Unterberger A. () Quantization, products and Poisson brackets.

In: Quantization and Non-holomorphic Modular : André Unterberger. We study the torus partition function of the SL(2,R)/U(1) SUSY gauged WZW model coupled to N=2 U(1) current. Starting from the path-integral formulation of the theory, we introduce an infra-red regularization which preserves good modular properties and discuss the decomposition of the partition function in terms of the N=2 characters of discrete (BPS) and continuous (non-BPS).

Discover Book Depository's huge selection of A Unterberger books online. Free delivery worldwide on over 20 million : A. Unterberger. Quantization and Quantization and Non-holomorphic Modular Forms book Modular Forms (Lecture Notes in Mathematics) by Andre Unterberger | Oct 2, Paperback Automorphic Distributions in the Plane and Modular Forms (Pseudo-Differential Operators Book 8) by André Unterberger eTextbook $ $.

Quantization and Quantization and Non-holomorphic Modular Forms book. Authors: Unterberger, André the former book deals with automorphic symbols, while in this one, it is the distributions to which the operators under consideration are applied that carry the arithmetic; in this way, L-functions, rather Brand: Birkhäuser Basel.

The starting point is a notion of modular distribution in the plane, which will be new to most readers and which, under the Radon transformation, relates to the classical notion of non-holomorphic modular form.

Holomorphic modular forms are also briefly considered, within a general scheme that addresses quantization theory and elementary but Author: André Unterberger. A class of non-holomorphic modular forms Francis Brown All Souls College, Oxford (IHES, Bures-Sur-Yvette) Modular forms are everywhere MPIM 22nd May 1/ Two motivations 1 Do there exist modular forms which correspond to mixed motives.

Today, mixed Tate motives over Z mainly. 2 String theory. Genus one closed superstring amplitudes. Graph. Pseudo-Differential Operators: Quantization and Signals - Ebook written by Hans G.

Feichtinger, Bernard Helffer, Michael Lamoureux, Nicolas Lerner, Joachim Toft. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Pseudo-Differential Operators: Quantization and Signals.

Quantization and Non-holomorphic Modular Forms, A. Unterberger, Lecture Notes in MathematicsSpringer Meromorphic Functions over non-Archimedean Fields, Pei-Chu Hu, Chung-Chun Yang, Mathematics and its applicationsKluwer Ebook Download PDF.

A Treatise On the Analytical Geometry of the Point, Line, Circle, and Conic Sections: Containing an Account of Its Most Recent Extensions: With Numerous Examples. Francis Brown: A class of non-holomorphic modular forms Abstract: I will define an elementary theory of non-holomorphic modular forms and describe some of its basic properties.

Within this family, there exists a class of functions which correspond to certain mixed motives. We give a sufficient condition of bounded growth for the non-holomorphic Eisenstein series on SL 2(ℤ). The C ∞-automorphic forms of bounded growth are introduced by Sturm (Duke Math. 48(2 Author: Takumi Noda.

RANK GENERATING FUNCTIONS AS WEAKLY HOLOMORPHIC MODULAR FORMS SCOTT AHLGREN AND STEPHANIE TRENEER Abstract. We study infinite families of generating functions involving the rank of the or-dinary partition function, which include as special cases many of the generating functions introduced by Atkin and Swinnerton-Dyer in the s.

We construct a distribution on R2, invariant under the linear action on R2 of the group Γ=SL(2,Z), whose decomposition into homogeneous terms depends on all non-holomorphic modular forms for the.

TITLE: Parallel text processing: alignment and use of translation corpora / edited by Jean Véronis. PUBLISHER: Dordrecht ; Boston: Kluwer Academic, c As another example, Miyake's book Modular Forms writes on p, "Automorphic functions and automorphic forms for modular groups are called modular functions and modular forms, respectively," and his definition of "modular group" seems to coincide with that of congruence subgroup.

Automorphic Pseudodifferential Analysis and Higher Level Weyl Calculi Author: André Unterberger Published by Birkhäuser Basel ISBN: DOI: / Table of Contents: Introduction Automorphic Distributions and the Weyl Calculus A Higher-level Weyl Calculus of Operators The Sharp Composition of Automorphic.

Discover Book Depository's huge selection of Andre Unterberger books online. Free delivery worldwide on over 20 million titles. QUADRATIC TWISTS AND THE COEFFICIENTS OF WEAKLY HOLOMORPHIC MODULAR FORMS STEPHANIE TRENEER weak Maass forms whose non-holomorphic part is the period integral of a single variable theta function.

Indeed, Brigmann and Ono [10] apply Theorem to a particular family of modular forms which can be built from Dedekind’s eta-function.

Siegel modular forms, we are concerned with non-holomorphic Siegel-Eisenstein series. The Koecher-Maass series associated with the non-holomorphic Siegel-Eisenstein series whose degree larger than two was studied by Arakawa, Suzuki, Ibukiyama-Katsurada, Sato-Ueno.

The overused word "quantization" refers to a variety of activities originating from several domains of mathematics or mathematical physics: quantum mechanics, representation theory or, more generally, harmonic analysis, pseudodifferential analysis.

It is our point of view that the most-embracing vantage point is the last one: since we fully realize that this may set us in a somewhat isolated Author: Andre Unterberger. Download Quantization and Non-holomorphic Modular Forms (Lecture Notes in Mathematics) Ebook Ebook Advances in Chemical Physics, Vol.

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The relationship between Jacobi forms and modular forms has appeared in many guises and stems back to important work on holomorphic Jacobi forms, which states that they have theta decompositions relating them to half-integral weight modular forms [20].

The situation for meromorphic positive index Jacobi forms well-understood as well; a meromorphic. Abstract: We introduce and study higher depth quantum modular forms. We construct two families of examples coming from rank two false theta functions, whose "companions" in the lower half-plane can be also realized both as double Eichler integrals and as non-holomorphic theta series having values of "double error" functions as by: 5.

Booktopia - Buy Number Theory books online from Australia's leading online bookstore. Discount Number Theory books and flat rate shipping of $ per online book order. The primary aim of this book is to create situations in which the zeta function, or other L-functions, will appear in spectral-theoretic questions.

A secondary aim is to connect pseudo-differential analysis, or quantization theory, to analytic number theory.

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Discount Integral Calculus & Equations books and flat rate shipping of $ per online book order. which is a mock modular form.

We use the Kontsevich-Soibelman wall-crossing formula to determine the jumps in the modified elliptic genus. Using the regularisation procedure for mock modular forms of Zwegers, modularity can be restored at the cost of holomorphicity.

We show that the non-holomorphic completion is due to bound states of single. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. $ do not map holomorphic differential forms to non-holomorphic or vice versa.

A coordinate change in our example would be any biholomorphic map of an open subset of $\mathbb{C}$ to another open subset of. This week's new book list. New Books Since Septem This list is updated every Thursday. Titles are arranged in call number order.

To view previous lists, see our archives page. TITLE = Quantization and non-holomorphic modular forms / Andr{}e Unterberger. sions of spaces of holomorphic second-order forms of even weight. We also establish a cohomological interpretation and prove an Eichler-Shimura-type isomorphism.

Introduction In the paper [KZ], Kleban and Zagier find that the study of crossing proba-bilities in percolation theory leads naturally to holomorphic second-order modular forms.

$\begingroup$ One thing that's constant in the study of automorphic and modular forms is the drive to classify the forms. It's hard to have a complete classification if one isn't sure what the simplest pieces are of whatever you're trying to classify, and the different ways of.

Quantization and Non-holomorphic Modular Forms, A. Unterberger La New Adult 3 Student CD, Ron Martinez Surviving Terrorism - Recognition and Response Guide to Chemical, Biological, Radiological and Nuclear Attacks, Alexander E Gowen.

Lecture Notes in Mathematics réponses. Attention: seules les premières sont affichées ci-dessous Gille, Philippe Quantization and non-holomorphic modular forms. - Springer Verlag, - (Lecture Notes in Mathematics; ). The red book of varieties and schemes. 2nd and expanded edition. Include the Michigan lectures ( Vounatsou P., Smith T.

- The book covers the main aspects of dynamic phenomena in confined magnetic structures on a level that researchers find a comprehensive compilation of the current status in. Palis, Carmo.

- (Lecture Notes in Mathematics)Geometry and Topology (, Springer) ISBN(s) We consider properties of modular graph functions, which are non-holomorphic modular functions associated with the Feynman graphs for a conformal scalar field theory on a two-dimensional torus. Such functions arise, for example, in the low energy expansion of genus-one Type II superstring amplitudes.Arkusz3 Arkusz2 Arkusz1 publication_title print_identifier online_identifier date_first_issue_online title_url first_author publisher_name publication_type.

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