Global Frobenius liftability I

On Ruelle–Perron–Frobenius Operators. I. Ruelle Theorem

We study Ruelle–Perron–Frobenius operators for locally expanding and mixing dynamical systems on general compact metric spaces associated with potentials satisfying the Dini condition. In this paper, we give a proof of the Ruelle Theorem on Gibbs measures. It is the first part of our research on the subject. The rate of convergence of powers of the operator will be presented in a forthcoming pa...

Gauss - Manin Systems , Brieskorn Lattices and Frobenius Structures ( I )

— We associate to any convenient nondegenerate Laurent polynomial f on the complex torus (C∗ )n a canonical Frobenius-Saito structure on the base space of its universal unfolding. According to the method of K. Saito (primitive forms) and of M. Saito (good basis of the Gauss-Manin system), the main problem, which is solved in this article, is the analysis of the Gauss-Manin system of f (or its u...

AVERAGE FROBENIUS DISTRIBUTION FOR INERTS IN Q(i)

Given an integer r, we consider the problem of enumerating the inert prime ideals p of Q(i) for which a given elliptic curve E has trace of Frobenius at p equal to r. We prove that on average the number of such prime ideals up to x is asymptotic to cr log log x where cr is an explicit constant computed in terms of an Euler product. This result is in accordance with the standard heuristics. This...

I. Global

Nearly Rational Frobenius Groups

In this paper, we study the structure of nite Frobenius groups whose non-rational or non-real irreducible characters are linear.