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Elliptic integrals, elliptic functions and modular forms in quantum field theory

Author: J Blümlein; Carsten Schneider; Peter Paule
Publisher: Cham, Switzerland : Springer, 2019.
Series: Texts and monographs in symbolic computation
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book includes review articles in the field of elliptic integrals, elliptic functions and modular forms intending to foster the discussion between theoretical physicists working on higher loop calculations and mathematicians working in the field of modular forms and functions and analytic solutions of higher order differential and difference equations.
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: J Blümlein; Carsten Schneider; Peter Paule
ISBN: 9783030044800 3030044807 3030044793 9783030044794 9783030044817 3030044815
OCLC Number: 1084726571
Description: 1 online resource (xiii, 509 pages) : illustrations (some color)
Contents: Intro; Preface; Contents; Contributors; Eta Quotients and Rademacher Sums; 1 Introduction; 2 Eta Quotients in Quantum Field Theory; 2.1 Atkin-Lehner Transformations of Eta Quotients; 2.2 Eichler Integrals of Eta Quotients for On-Shell Sunrise Integrals; 2.3 Eichler Integrals for Quasi-periods at Level 6; 3 Rademacher Sums for Fourier Coefficients of Eta Quotients; 3.1 Genus 0; 3.2 Further Examples of Integer Sequences; 3.3 Genus 1; 3.4 Rational Rademacher Sums; 3.5 Genus 2; 3.6 Genus 3; 3.7 Genus 4; 3.8 Genus 5; 3.9 Genus 6; 3.10 Genus 7; 3.11 Genus 8; 3.12 Genus 13; 3.13 Remarks 4 ConclusionsReferences; On a Class of Feynman Integrals Evaluating to Iterated Integrals of Modular Forms; 1 Introduction; 2 Periodic Functions and Periods; 3 Elliptic Curves; 4 Modular Forms; 5 Iterated Integrals; 6 Precision Calculations; 7 Picard-Fuchs Operators; 8 Feynman Integrals Evaluating to Iterated Integrals of Modular Forms; 9 Conclusions; References; Iterative Non-iterative Integrals in Quantum Field Theory; 1 Introduction; 2 Second-Order Differential Equations and 2F1 Solutions; 3 Iterative Non-iterative Integrals; 4 Numerical Representation
Series Title: Texts and monographs in symbolic computation
Responsibility: Johannes Blümlein, Carsten Schneider, Peter Paule, editors.

Abstract:

This book includes review articles in the field of elliptic integrals, elliptic functions and modular forms intending to foster the discussion between theoretical physicists working on higher loop calculations and mathematicians working in the field of modular forms and functions and analytic solutions of higher order differential and difference equations.

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"The book is explicitly concerned with `the mathematics of modular forms [as it is] of central importance for the analytic solution of Feynman diagrams,' but modular formers should be equally Read more...

 
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