Computations concerning the conjecture of Mertens.
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.
Conditional bounds for small prime solutions of linear equations.
Conjugacy class lengths of metanilpotent groups
Connection between Schinzel’s conjecture and divisibility of the class number
Consecutive integers in algebraic number fields.
Consecutive primes in tuples
In a stunning new advance towards the Prime k-Tuple Conjecture, Maynard and Tao have shown that if k is sufficiently large in terms of m, then for an admissible k-tuple of linear forms in ℤ[x], the set contains at least m primes for infinitely many n ∈ ℕ. In this note, we deduce that contains at least m consecutive primes for infinitely many n ∈ ℕ. We answer an old question of Erdős and Turán by producing strings of m + 1 consecutive primes whose successive gaps form an increasing (resp....
Consecutive square-free values of the type ,
We show that for any given integer there exist infinitely many consecutive square-free numbers of the type , . We also establish an asymptotic formula for such that , are square-free. The method we used in this paper is due to Tolev.
Consequences of a theorem of Erdős-Prachar.
Construction of normal numbers via pseudo-polynomial prime sequences
We construct normal numbers in base q by concatenating q-ary expansions of pseudo-polynomials evaluated at primes. This extends a recent result by Tichy and the author.
Continued fractions of period five and real quadratic fields of class number one
Contributions to the Erdös-Szemerédi theory of sieved integers
Contributions to the theory of Kummer extensions
Convoluted convolved Fibonacci numbers.
Convolutions and Mean Square Estimates of Certain Number-theoretic Error Terms
Correction au travail "Sur la densité de certains ensembles de multiples, 1", (Acta Arith. 69 (1995), 121-152)
Correction to my paper «Sull'analogo della formula di Selberg nei corpi di funzioni»
This Note completes and corrects a preceding Lincean Note by introducing through a tauberian theorem an appropriate condition which removes a counter-example provided by Dr. Zhang.
Correction to our paper 'On the average order of an arithmetical function'