Periods and Lefschetz zeta functions

Lefschetz formulae and zeta functions

The connection between Lefschetz formulae and zeta function is explained. As a particular example the theory of the generalized Selberg zeta function is presented. Applications are given to the theory of Anosov flows and prime geodesic theorems.

F eb 2 00 3 PERIODS AND IGUSA ZETA FUNCTIONS

We show that the coefficients in the Laurent series of Igusa Zeta functions I(s) = ∫ C fω are periods. This will be used to show in a subsequent paper (by P. Brosnan) that certain numbers occurring in Feynman amplitudes (upto gamma factors) are periods. INTRODUCTION In their paper [8], Kontsevich and Zagier give an elementary definition of a period integral as an absolutely convergent integral ...

Periods for Holomorphic Maps via Lefschetz Numbers

In this note we are concerned with fixed point theory for holomorphic self maps on complex manifolds. After the well-known Schwarz lemma on the unit disk, which assumes a fixed point, the Pick theorem was proved in [8]. This can be extended to a Pick-type theorem on hyperbolic Riemann surfaces as is shown in [5, 7]. For a more general type of space: open, connected and bounded subsets of a Bana...

Multiple Zeta Values and Periods of Moduli

Periods of Mirrors and Multiple Zeta Values

In a recent paper, A. Libgober showed that the multiplicative sequence {Qi(c1, . . . , ci)} of Chern classes corresponding to the power series Q(z) = Γ(1 + z)−1 appears in a relation between the Chern classes of certain Calabi-Yau manifolds and the periods of their mirrors. We show that the polynomials Qi can be expressed in terms of multiple zeta values. 1. The multiplicative sequence In [6], ...