Chebyshev's method for number fields
We give an elementary proof of an explicit estimate for the number of primes splitting completely in an extension of the rationals. The proof uses binomial coefficents and extends Chebyshev's classical approach.
Chen's double sieve, Goldbach's conjecture and the twin prime problem, 2
Chen's double sieve, Goldbach's conjecture and the twin prime problem
Class numbers of elliptic function fields and the distribution of prime numbers
Compact integers and factorials
Consecutive integers in algebraic number fields.
Consequences of a theorem of Erdős-Prachar.
Correction to the paper "The divisor problem for (k, r)-integers. II".
Correction to the paper "The number of k-free and k-ary divisors of m which are prime to n".
Corrigendum to my paper "On twin almost primes" and an addendum on Selberg's sieve
Corrigendum zur Arbeit „Über die reellen Nullstellen der Dirichletschen L-Reihen"
Counting monic irreducible polynomials in for which order of is odd
Hasse showed the existence and computed the Dirichlet density of the set of primes for which the order of is odd; it is . Here we mimic successfully Hasse’s method to compute the density of monic irreducibles in for which the order of is odd. But on the way, we are also led to a new and elementary proof of these densities. More observations are made, and averages are considered, in particular, an average of the ’s as varies through all rational primes.