Diophantine number theory is an active area that has seen tremendous growth over the past
century, and in this theory unit equations play a central role. This comprehensive treatment …

Lech proved in 1953 that the set of zeroes of a linear recurrence sequence in a field of
characteristic 0 is the union of a finite set and finitely many infinite arithmetic progressions …

Let K be a field of characteristic p> 0 and let f (t 1,…, td) be a power series in d variables with
coefficients in K that is algebraic over the field of multivariate rational functions K (t 1,…, td) …

There are three aims of this note. The first one is to report some advances around the
dynamical Mordell-Lang (= DML) conjecture. Second, we generalize some known results …

The conjectures associated with the names of Zilber-Pink greatly generalize results
associated with the names of Manin-Mumford and Mordell-Lang, but unlike the latter they …

Let K be a field of positive characteristic. When V is a linear variety in Kn and G is a finitely
generated subgroup of K*, we show how to compute the set V∩ Gn effectively using heights …

THE DYNAMICAL MORDELL–LANG CONJECTURE FOR ENDOMORPHISMS OF SEMIABELIAN
VARIETIES DEFINED OVER FIELDS OF POSITIVE CHARACTERISTI Page 1 J. Inst. Math …

THE MORDELL–LANG CONJECTURE FOR SEMIABELIAN VARIETIES DEFINED OVER
FIELDS OF POSITIVE CHARACTERISTIC Page 1 Bull. Aust. Math. Soc. (First published online …

We determine the structure of the intersection of a finitely generated subgroup of a
semiabelian variety $ G $ defined over a finite field with a closed subvariety $ X\subset G …

Let $ K $ be an algebraically closed field of prime characteristic $ p $, let $ N\in\mathbb {N}
$, let $\Phi:\mathbb {G} _m^ N\longrightarrow\mathbb {G} _m^ N $ be a self-map defined …