Feynman integrals and critical modular $L$-values
نویسندگان
چکیده
منابع مشابه
Moments of Elliptic Integrals and Critical L-values
We compute the critical L-values of some weight 3, 4, or 5 modular forms, by transforming them into integrals of the complete elliptic integral K. In doing so, we prove closed form formulas for some moments of K ′3. Many of our L-values can be expressed in terms of Gamma functions, and this also gives new lattice sum evaluations.
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We often deal with products of many propagator factors in loop integrals. The trick is to combine many propagators into a single fraction so that the four-momentum integration can be done easily. This is done commonly using so-called Feynman parameters. We rewrite the product of propagators 1 (A 1 + ii)(A 2 + ii) · · · (A n + ii) , (1) where A i has the form of p 2 − m 2. The sign of A i is not...
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ژورنال
عنوان ژورنال: Communications in Number Theory and Physics
سال: 2016
ISSN: 1931-4523,1931-4531
DOI: 10.4310/cntp.2016.v10.n1.a5