On the density of some sets of primes, II
On the density of some sets of primes, IV
On the difference between consecutive prime numbers
On the Difference Between Consecutive Primes.
On the Difference between Consecutive Primes.
On the difference between consecutive squarefree integers
On the distributation of p ... modulo one.
On the distribution of amicable numbers.
On the distribution of Hawkins’ random “primes”
Hawkins introduced a probabilistic version of Erathosthenes’ sieve and studied the associated sequence of random “primes” . Using various probabilistic techniques, many authors have obtained sharp results concerning these random “primes”, which are often in agreement with certain classical theorems or conjectures for prime numbers. In this paper, we prove that the number of integers such that is almost surely equivalent to , for a given fixed integer . This is a particular case of a recent...
On the distribution of integers with a given number of prime factors
On the distribution of the zeros of Dirichlet's L-functions
On the error term of an asymptotic formula of Ramanujan
On the error term of the logarithm of the lcm of a quadratic sequence
We study the logarithm of the least common multiple of the sequence of integers given by . Using a result of Homma [5] on the distribution of roots of quadratic polynomials modulo primes we calculate the error term for the asymptotics obtained by Cilleruelo [3].
On the exceptional set for the -twin primes problem
On the first sign change in Mertens' theorem
The function is known to change sign infinitely often, but so far all calculated values are positive. In this paper we prove that the first sign change occurs well before exp(495.702833165).
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 an arithmetical progression. II
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 factors of polynomials at integer points