Related papers: Schanuel Type Conjectures and Disjointness

During the Arizona Winter School 2008 (held in Tucson, AZ) we worked on the following problems: a) (Expanding a remark by S. Lang). Define $E_0 = \overline{\mathbb{Q}}$ Inductively, for $n \geq 1$, define $E_n$ as the algebraic closure of…

We study solutions of exponential polynomials over the complex field. Assuming Schanuel's conjecture we prove that certain polynomials have generic solutions in the complex field.

Inspired by work done for systems of polynomial exponential equations, we study systems of equations involving the modular $j$ function. We show general cases in which these systems have solutions, and then we look at certain situations in…

In this paper we use tools from set theory and the uncountable categoricity of Zilber's pseudo-exponential field to show that Zilber's field is isomorphic to the complex field with (standard) exponentiation and hence Schanuel's conjecture…

The algebra of exponential fields and their extensions is developed. The focus is on ELA-fields, which are algebraically closed with a surjective exponential map. In this context, finitely presented extensions are defined, it is shown that…

Pseudoexponential fields are exponential fields similar to complex exponentiation satisfying the Schanuel Property, which is the abstract statement of Schanuel's Conjecture, and an adapted form of existential closure. Here we show that if…

The paper [GLZ] "L-functions of Carlitz modules, resultantal varieties and rooted binary trees" is devoted to a description of some resultantal varieties related to L-functions of Carlitz modules. It contains a conjecture that some of these…

In [1], J. Ax proved a transcendency theorem for certain differential fields of characteristic zero: the differential counterpart of the still open Schanuel's conjecture about the exponential function over the field of complex numbers [11,…

Schanuel Conjecture contains all ``reasonable" statements that can be made on the values of the exponential function. In particular it implies the Lindemann-Weierstrass Theorem. In my Ph.D. I showed that Schanuel Conjecture has a…

In this article we study an abelian analogue of Schanuel's conjecture. This conjecture falls in the realm of the generalised period conjecture of Y. Andr{\'e}. As shown by C. Bertolin, the generalised period conjecture includes Schanuel's…

In this paper, we prove that a pseudoexponential field has continuum many non-isomorphic countable real closed exponential subfields, each with an order preserving exponential map which is surjective onto the nonnegative elements. Indeed,…

We consider the theory of algebraically closed fields of characteristic zero with multivalued operations $x\mapsto x^r$ (raising to powers). It is in fact the theory of equations in exponential sums. In an earlier paper we have described…

In this paper we prove that assuming Schanuel's conjecture, an exponential polynomial in one variable over the algebraic numbers has only finitely many algebraic solutions. This implies a positive answer to Shapiro's conjecture for…

We introduce and discuss a variant of Schanuel conjecture in the framework of the Carlitz exponential function over Tate algebras and allied functions. Another purpose of the present paper is to widen the horizons of possible investigations…

Assuming Schanuel's conjecture, we prove that any polynomial exponential equation in one variable must have a solution that is transcendental over a given finitely generated field. With the help of some recent results in Diophantine…

In this paper we prove a conjecture regarding the form of the Born-Infeld Lagrangian with a U(1)^2n gauge group after the elimination of the auxiliary fields. We show that the Lagrangian can be written as a symmetrized trace of Lorentz…

For a subgroup of $PGL(2,q)$ we show how some irreducible polynomials over $\mathbb{F}_q$ arise from the field of invariant rational functions. The proofs rely on two actions of $PGL(2,F)$, one on the projective line over a field $F$ and…

It is expected that Schanuel's Conjecture contains all ``reasonable" statements that can be made on the values of {\em the exponential function}. In particular it implies the Lindemann-Weierstrass Theorem and the Conjecture on algebraic…

In this article we study Semi-abelian analogues of Schanuel conjecture. As showed by the first author, Schanuel Conjecture is equivalent to the Generalized Period Conjecture applied to 1-motives without abelian part. Extending her methods,…

Let $E/F$ be a quadratic extension of p-adic fields. We prove that every smooth irreducible ladder representation of the group $GL_n(E)$ which is contragredient to its own Galois conjugate, possesses the expected distinction properties…