On the Graded Ring of Hubert Modular Forms Associated with Q (|..5).
On the graded rings of modular forms
On the greatest prime divisor of quadratic sequences
On the greatest prime factor of for a prime p and other expressions
On the greatest prime factor of a cubic polynomial.
On the greatest prime factor of
On the greatest prime factor of (ab + 1) (ac + 1) (bc + 1)
On the greatest prime factor of (ab + 1)(bc + 1)(ca + 1)
On the greatest prime factor of an arithmetical progression. II
On the greatest prime factor of Markov pairs
On the greatest prime factor of
There exist infinitely many integers such that the greatest prime factor of is at least . The proof is a combination of Hooley’s method – for reducing the problem to the evaluation of Kloosterman sums – and the majorization of Kloosterman sums on average due to the authors.
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.