Elliptic integrals, elliptic functions and modular forms in quantum field theory /
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| Imprint: | Cham, Switzerland : Springer, 2019. |
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| Description: | 1 online resource (xiii, 509 pages) : illustrations (some color) |
| Language: | English |
| Series: | Texts & monographs in symbolic computation, 0943-853X Texts and monographs in symbolic computation, |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11781523 |
Table of 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