Linear Recurrence Sequences

On the integer solutions of exponential equations in function fields

“…- [BMZ], §5.) We also note that the conclusions in [Schm,310], or [BMZ, Thm. [ESS], who give quite remarkable estimates; also, Evertse and Gy6ry [EG] have studied a function-field analogue. [BrM] (see also [Z] [EZ].…”

“…(See also [Schm,§10] for an analogous approach.) The purpose of the present paper is to carry out a similar analysis for polynomial-exponential equations in several variables.…”

“…We stress that the alluded proofs do not work automatically for several variables; we briefly outline the main points. The approach in [BMZ] or [Schm,§10] (See §2 and Remark 2 below. )…”

The orbit intersection problem for linear spaces and semiabelian varieties

“…In Section 3, we present the proof of Theorem 1.6 which requires a careful analysis of a certain system of polynomialexponential equations in two variables. Some results on polynomial-exponential equations are given in the next section following Schmidt's exposition [Sch03]. In Section 4, Theorem 1.4 is reduced to Theorem 1.6 thanks to the use of the p-adic exponential map for an appropriate choice of the prime p.…”

“…Some classical results. A large part of this subsection follows the notation from Schmidt's article [Sch03]. All the sequences considered in this section are sequences of complex numbers.…”