On the greatest prime factor of
On the greatest prime factors of polynomials at integer points
On the group .
On the group of circular units of any compositum of quadratic fields
On the group orders of elliptic curves over finite fields
On the growth of a van der Waerden-like function.
On the growth of averaged Weyl sums for rigid rotations
On the growth rate of generalized Fibonacci numbers.
On the Győry-Sárközy-Stewart conjecture in function fields
We consider function field analogues of the conjecture of Győry, Sárközy and Stewart (1996) on the greatest prime divisor of the product for distinct positive integers , and . In particular, we show that, under some natural conditions on rational functions , the number of distinct zeros and poles of the shifted products and grows linearly with if . We also obtain a version of this result for rational functions over a finite field.
On the Hasse norm principle.
On the Hasse principle for Witt groups.
On the Hausdorff dimension of the expressible set of certain sequences
On the height constant for curves of genus two
On the height constant for curves of genus two, II
On the height of algebraic numbers with real conjugates
On the height of cyclotomic polynomials
On the height of the Sylvester resultant.
On the heights of power digraphs modulo
A power digraph, denoted by , is a directed graph with as the set of vertices and as the edge set. In this paper we extend the work done by Lawrence Somer and Michal Křížek: On a connection of number theory with graph theory, Czech. Math. J. 54 (2004), 465–485, and Lawrence Somer and Michal Křížek: Structure of digraphs associated with quadratic congruences with composite moduli, Discrete Math. 306 (2006), 2174–2185. The heights of the vertices and the components of for and are determined....
On the heights of totally -adic numbers
Bombieri and Zannier established lower and upper bounds for the limit infimum of the Weil height in fields of totally -adic numbers and generalizations thereof. In this paper, we use potential theoretic techniques to generalize the upper bounds from their paper and, under the assumption of integrality, to improve slightly upon their bounds.
On the higher mean over arithmetic progressions of Fourier coefficients of cusp forms
Let be the nth normalized Fourier coefficient of a holomorphic or Maass cusp form f for SL(2,ℤ). We establish the asymptotic formula for the summatory function as x → ∞, where q grows with x in a definite way and j = 2,3,4.