Frobenius map and the p -adic Gamma function

THE TRACE OF FROBENIUS OF ELLIPTIC CURVES AND THE p-ADIC GAMMA FUNCTION

We define a function in terms of quotients of the p-adic gamma function which generalizes earlier work of the author on extending hypergeometric functions over finite fields to the p-adic setting. We prove, for primes p > 3, that the trace of Frobenius of any elliptic curve over Fp, whose jinvariant does not equal 0 or 1728, is just a special value of this function. This generalizes results of ...

P-adic Superspaces and Frobenius

The notion of a p-adic superspace is introduced and used to give a transparent construction of the Frobenius map on p-adic cohomology of a smooth projective variety over Z p (the ring of p-adic integers). This article partially intersects with [9]; it contains the proofs omitted in [9] as well as some investigations into the important notion of a prorepresentable p-adic superspace.

Multivariate P-adic L-function

In the recent, many mathematicians studied the multiple zeta function in the complex number field. In this paper we construct the p-adic analogue of multiple zeta function which interpolates the generalized multiple Bernoulli numbers attached to χ at negative integers. §1. Introduction Let p be a fixed prime. Throughout this paper Z p , Q p , C and C p will, respectively, denote the ring of p-a...

The “missing” p-adic L-function – DRAFT

Inverting the Frobenius Map

The famous Frobenius characteristic map is a bijection from the space of characters of a symmetric group S n to the space of homogeneous symmetric functions of degree n. In this note, we prove a formula for the inverse map. More precisely, we express the generating function for the values of an arbitrary virtual character of S n in terms of the symmetric function which is the Frobenius image of...