PERIOD INTEGRALS AND TAUTOLOGICAL SYSTEMS

Let X be a non-singular projective carve of genus g, defined over a field K of characteristic zero. Recall that a meromorphic differential is said to be of the second kind if all of

The goal of this paper is to construct a regular holonomic differential system that governs the p-th derivative of period integrals for each p ∈ Z.. By the preceding corollary,

Finally, our realization of R allows us to show that the period inte- grals are governed by a tautological system (Theorem 8.8), or a certain enhanced version of it (Theorem 8.9.)

A tautological system, introduced in [17][18], arises as a regular holonomic system of partial differential equations that governs the period integrals of a family of

Since all (except the Riemann zeta function) of those special functions are solutions to ordinary differential equations, it is natural to consider the higher dimensional analogues

Basically the idea is to require enough smoothness on the Fourier transform of the kernel (i.e. We will prove a vector valued multiplier theorem when

Furthermore, when the order is finite, the essential extension = {X, A} , where A is a differential polynomial with coefficients obtained through a rational solution of a

Every part of physics offers examples of non-stability phenomena, but probably nowhere are they so plentiful and worthy of study as in the realm of quantum theory6. The present