Communications in Number Theory and Physics

Volume 6 (2012)

Number 1

Feynman graph integrals and almost modular forms

Pages: 129 – 157

DOI: http://dx.doi.org/10.4310/CNTP.2012.v6.n1.a3

Author

Si Li (Mathematics Department, Northwestern University, Evanston, Illinois)

Abstract

We introduce a type of graph integrals on elliptic curvesfrom the heat kernel. We show that such graph integralshave modular properties under the modular group $SL(2,\Z)$, and prove the polynomial nature of theanti-holomorphic dependence.

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