Let F(X, Y ) = s i=0 ai Xri Yr−ri ∈ Z[X, Y ] be a form of degree r = rs ≥ 3, irreducible over Q and having at most s + 1 non-zero coefficients. Mueller and Schmidt showed that the number of solutions of the Thue ...

Let q be an integer ≥2 and let Sq(n) denote the sum of digits of n in base q. For α=[0;1,m¯¯¯¯¯¯¯¯¯], m≥2, let Sα(n) denote the sum of digits in the Ostrowski α-representation of n. Let m1,m2≥2 be integers with gcd(q− ...

We give improved upper bounds for the number of solutions of the Thue equation F(x; y) = h where F is an irreducible binary form of degree 3:

Nora and Wanda are two players who choose coefficients of a degree-d polynomial from some fixed unital commutative ring R. Wanda is declared the winner if the polynomial has a root in the ring of fractions of R and Nora ...

Following a method originally due to Siegel, we establish upper bounds for the number of primitive integer solutions to inequalities of the shape 0<|F(x,y)|≤h, where F(x,y)=(αx+βy)r−(γx+δy)r∈Z[x,y], α, β, γ and δ are ...