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

Description

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. Front Matter ....Pages i-xiii Eta Quotients and Rademacher Sums (Kevin Acres, David Broadhurst)....Pages 1-27 On a Class of Feynman Integrals Evaluating to Iterated Integrals of Modular Forms (Luise Adams, Stefan Weinzierl)....Pages 29-49 Iterative Non-iterative Integrals in Quantum Field Theory (Johannes Blümlein)....Pages 51-77 Analytic Continuation of the Kite Family (Christian Bogner, Armin Schweitzer, Stefan Weinzierl)....Pages 79-91 A Four-Point Function for the Planar QCD Massive Corrections to Top-Antitop Production in the Gluon-Fusion Channel (Roberto Bonciani, Matteo Capozi, Paul Caucal)....Pages 93-106 From Modular Forms to Differential Equations for Feynman Integrals (Johannes Broedel, Claude Duhr, Falko Dulat, Brenda Penante, Lorenzo Tancredi)....Pages 107-131 One-Loop StringScatteringAmplitudes as Iterated Eisenstein Integrals (Johannes Broedel, Oliver Schlotterer)....Pages 133-159 Expansions at Cusps and Petersson Products in Pari/GP (Henri Cohen)....Pages 161-181 CM Evaluations of the Goswami-Sun Series (Madeline Locus Dawsey, Ken Ono)....Pages 183-193 Automatic Proof of Theta-Function Identities (Jie Frye, Frank Garvan)....Pages 195-258 The Generators of all Polynomial Relations Among Jacobi Theta Functions (Ralf Hemmecke, Cristian-Silviu Radu, Liangjie Ye)....Pages 259-268 Numerical Evaluation of Elliptic Functions, Elliptic Integrals and Modular Forms (Fredrik Johansson)....Pages 269-293 Multi-valued Feynman Graphs and Scattering Theory (Dirk Kreimer)....Pages 295-325 Interpolated Sequences and Critical L-Values of Modular Forms (Robert Osburn, Armin Straub)....Pages 327-349 Towards a Symbolic Summation Theory for Unspecified Sequences (Peter Paule, Carsten Schneider)....Pages 351-390 Differential Equations and Dispersion Relations for Feynman Amplitudes (Ettore Remiddi)....Pages 391-414 Feynman Integrals, Toric Geometry and Mirror Symmetry (Pierre Vanhove)....Pages 415-458 Modular and Holomorphic Graph Functions from Superstring Amplitudes (Federico Zerbini)....Pages 459-484 Some Algebraic and Arithmetic Properties of Feynman Diagrams (Yajun Zhou)....Pages 485-509