We prove that assuming the Colmez conjecture and “no Siegel zeros” conjecture, stable Faltings height of a CM abelian variety over number field is less than or equal to logarithm root discriminant definition times an effective constant depending only on dimension variety. In view fact for fields, averaged fields with no complex quadratic subfields are already proved, we unconditional analogues ...

We report on an implementation within GiNaC to evaluate iterated integrals related elliptic Feynman numerically arbitrary precision the region of convergence series expansion integrand. The includes modular forms as well involving Kronecker coefficient functions g ( k ) z , ? . For in d? and dz are implemented. This multiple polylogarithms. Note: program uploaded CPC Library is full program, or...

In this paper we introduce the concept of Abelian integrals in differential equations for an arbitrary vector bundle on P1 with a meromorphic connection. In this general context we give an upper bound for the numbers we are looking for. Let V be a locally free sheaf (vector bundle) of rank α on P and D = ∑r i=1 mici be a positive divisor in P , i.e. all ci’s are positive. We denote by C the set...