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  • © 2019

Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory

  • Presents up-to-date reviews on modular forms and functions and their use in particle physics

  • Combines knowledge from mathematical physics and mathematics

  • Written by international authors

Part of the book series: Texts & Monographs in Symbolic Computation (TEXTSMONOGR)

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xiii
  2. Eta Quotients and Rademacher Sums

    • Kevin Acres, David Broadhurst
    Pages 1-27
  3. Analytic Continuation of the Kite Family

    • Christian Bogner, Armin Schweitzer, Stefan Weinzierl
    Pages 79-91
  4. From Modular Forms to Differential Equations for Feynman Integrals

    • Johannes Broedel, Claude Duhr, Falko Dulat, Brenda Penante, Lorenzo Tancredi
    Pages 107-131
  5. One-Loop String Scattering Amplitudes as Iterated Eisenstein Integrals

    • Johannes Broedel, Oliver Schlotterer
    Pages 133-159
  6. CM Evaluations of the Goswami-Sun Series

    • Madeline Locus Dawsey, Ken Ono
    Pages 183-193
  7. Automatic Proof of Theta-Function Identities

    • Jie Frye, Frank Garvan
    Pages 195-258
  8. The Generators of all Polynomial Relations Among Jacobi Theta Functions

    • Ralf Hemmecke, Cristian-Silviu Radu, Liangjie Ye
    Pages 259-268
  9. Interpolated Sequences and Critical L-Values of Modular Forms

    • Robert Osburn, Armin Straub
    Pages 327-349
  10. Towards a Symbolic Summation Theory for Unspecified Sequences

    • Peter Paule, Carsten Schneider
    Pages 351-390

About this book

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. 

Reviews

“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 interested in the material offered in this compendium.” (Michael Berg, MAA Reviews, May 19, 2019)

Editors and Affiliations

  • Deutsches Elektronen-Synchrotron, DESY, Zeuthen, Germany

    Johannes Blümlein

  • Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Linz, Austria

    Carsten Schneider, Peter Paule

Bibliographic Information

Buy it now

Buying options

eBook USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access