Communications in Number Theory and Physics
Volume 6 (2012)
Feynman graph integrals and almost modular forms
Pages: 129 – 157
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.