Biases in the Shanks-Rényi prime number race.
Bombieri's theorem in short intervals
Bombieri's theorem in short intervals. II.
Bombieri-Vinogradov type theorems for sparse sets of moduli
Carmichael numbers composed of primes from a Beatty sequence
Let α,β ∈ ℝ be fixed with α > 1, and suppose that α is irrational and of finite type. We show that there are infinitely many Carmichael numbers composed solely of primes from the non-homogeneous Beatty sequence . We conjecture that the same result holds true when α is an irrational number of infinite type.
Chebotarev sets
We consider the problem of determining whether a set of primes, or, more generally, prime ideals in a number field, can be realized as a finite union of residue classes, or of Frobenius conjugacy classes. We give necessary conditions for a set to be realized in this manner, and show that the subset of primes consisting of every other prime cannot be expressed in this way, even if we allow a finite number of exceptions.
Chebyshev's bias.
Computing higher rank primitive root densities
We extend the "character sum method" for the computation of densities in Artin primitive root problems given by Lenstra and the authors to the situation of radical extensions of arbitrary rank. Our algebraic set-up identifies the key parameters of the situation at hand, and obviates the lengthy analytic multiplicative number theory arguments that used to go into the computation of actual densities. It yields a conceptual interpretation of the formulas obtained, and enables us to extend their range...
Concentration function of additive functions on shifted twin primes
Concentration function of additive functions on shifted twin primes
0. Introduction. The content of this paper is part of the author's Ph.D. thesis. The two new theorems in this paper provide upper bounds on the concentration function of additive functions evaluated on shifted γ-twin prime, where γ is any positive even integers. Both results are generalizations of theorems due to I. Z. Ruzsa, N. M. Timofeev, and P. D. T. A. Elliott.
Correction to the paper "On a kind of uniform distribution of values of multiplicative functions in residue classes", Acta Arithmetica 31(1976), pp. 291-294
Corrigendum zur Arbeit „Über die reellen Nullstellen der Dirichletschen L-Reihen"
Dirichlet theorems and prime number hypotheses of a conditional Goldbach theorem.
Distribution of coefficients of Eisenstein series in residue classes
Distribution of values of multiplicative functions in residue classes.
Distribution of Values of ...(n) in Residue Classes.
Distribution of zeros of Dirichlet L-functions and the least prime in an arithmetic progression
Double recurrence and almost sure convergence.
Důkaz věty, že existuje nekonečně mnoho kmenných čísel , je-li kmenné
Écarts entre nombres premiers successifs
Le théorème des nombres premiers dit que la distance entre deux nombres premiers consécutifs est, en moyenne, de l’ordre de . Récemment, D. Goldston, J. Pintz et C. Yıldırım sont parvenus à démontrer que la distance normalisée pouvait devenir arbitrairement petite, améliorant spectaculairement les résultats connus auparavant. Sous des hypothèses considérées comme raisonnables, ils parviennent à montrer que infiniment souvent. Leur méthode est une très jolie application d’idées inspirée par...