Alladi Ramakrishnan Hall

Frobenius constants for families of elliptic curves

Bidisha Roy

SNS, Pisa , Italy

{\it Periods} are complex numbers given as values of integrals of algebraic functions defined over domains, bounded by algebraic equations and inequalities with coefficients in $\mathbb{Q}$. In this talk, we will deal with a class of periods, {\it Frobenius constants}, arising as matrix entries of the monodromy representations of certain geometric differential operators. More precisely, we will consider seven special Picard - Fuchs type second order linear differential operators corresponding to families of elliptic curves. Using periods of modular forms, we will witness some of these Frobenius constants in terms of zeta values. This is a joint work with Masha Vlasenko.