Note on Coleman's formula for the absolute Frobenius on Fermat curves

Abstract

Coleman calculated the absolute Frobenius on Fermat curves explicitly. In this paper we show that a kind of $p$-adic continuity implies a large part of his formula. To do this, we study a relation between functional equations of the ($p$-adic) gamma function and monomial relations on ($p$-adic) CM-periods.

arXiv comment18 pages, to appear in Annales de l'Institut Fourier