Some properties of analytic difference fields

We prove formally that the first order theory of algebraically closed fields enjoy quantifier elimination, and hence is decidable.. This proof is organized in two

After defining an abstract structure of discrete real closed field and the elementary theory of real roots of polynomials, we describe the formalization of an algebraic proof

In Section 3 we introduce Artin motives with coefficients in a number field E in terms of representations of the Ga- lois group, determine when the Q-dimension of the left-hand side

When the valuation on k is non trivial we use the fact that ACV F , the theory of algebraically closed (non trivially) valued fields, has quantifier elimination.. It is a classical

We prove new explicit formulas for the p-adic L-functions of totally real number fields and show how these formulas can be used to compute values and representations of

The problem of electron scattering by one electron targets in a magnetic field is discussed, and it is shown that the first Born approximation is valid for all energies

We are going to prove in the next section that the faces of every largely continuous precell mod N are still largely continuous precells mod the same N (see Proposition 3.11). ,

At the end of the article, we discuss sufficient conditions for this property to hold for families of hypoelliptic vector fields, based either on the order m of the H¨ormander