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arxiv: 1112.4015 · v2 · pith:M6KZZH7Gnew · submitted 2011-12-17 · 🧮 math.NT · hep-th· math.CO

Feynman Graph Integrals and Almost Modular Forms

classification 🧮 math.NT hep-thmath.CO
keywords graphintegralsmodularalmostanti-holomorphiccurvesdependenceelliptic
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We introduce a type of graph integrals on elliptic curves from the heat kernel. We show that such graph integrals have modular properties under the modular group $SL(2, \Z)$, and prove the polynomial nature of the anti-holomorphic dependence.

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