Elliptic integrals, elliptic functions and modular forms in quantum field theory. (2019)

• Record Type: Book
• Further Information: Note: Johannes Blümlein, Carsten Schneider, Peter Paule, editors.
• Editors: Blümlein, J (Johannes); Schneider, Carsten; Paule, Peter
• 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
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2019
• Extent: 1 online resource (xiii, 509 pages), illustrations (some color)
• Subjects: 515/.983; Elliptic functions; Forms, Modular; Quantum field theory; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783030044800; 3030044807
• Related ISBNs: 9783030044794
• Notes: Note: Online resource; title from PDF title page (SpringerLink, viewed February 7, 2019).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.