Given a prime p, the Fermat quotient qp(u) of u with gcd(u, p)= 1 is defined by the conditions qp(u)≡ u p−1 − 1 p mod p, 0≤ qp(u)≤ p − 1. We derive a new bound on multiplicative character sums with Fermat quotients qp(`) at prime arguments `. 2010 Mathematics subject classification: primary 11A07; secondary 11L40, 11N25.

Given a non-negative integer k, we construct a lattice 3-simplex P with the following property: The affine semigroup QP associated to P is not normal, and every element q ∈ QP \ QP has lattice distance at least k above every facet of QP .

A Mathematical model has been considered to study the reflection and refraction phenomenon of plane wave at the interface of an isotropic liquid medium and a triclinic (anisotropic) half-space. The incident plane qP wave generates three types of reflected waves namely quasi-P (qP), quasi-SV (qSV) and quasi-SH (qSH) waves in the tric...

Soit p un nombre premier impair, K = Qp et soient Kn = Qp(μpn) le corps des racines p-ièmes de l’unité dans une clôture algébriqueQp de Qp, K∞ la réunion des Kn et G∞ = Gal(K∞/K). Soit une courbe elliptique E définie sur Qp. Si E(Kn) est le groupe des points de E définis sur Kn, la limite projective des E(Kn) pour les applications de trace a d’abord été étudiée lorsque E a bonne réduction ordin...

Fix an odd prime p, an algebraic closure Qp, and an isomorphism C ∼ → Qp. Fix an integer N ≥ 1 prime to p, and let T be the polynomial algebra over Z generated by the operators T!, ! ! Np, Up and 〈d〉 , d ∈ (Z/NZ). Set W = Spf(Zp[[Zp ]]), and let W = W rig be the rigid analytic space of characters of Zp together with its universal character χW : Z × p → O(W ) ; we embed Z in W (Qp) by mapping k ...