#### 79 Citations

Almost‐prime values of polynomials at prime arguments

- Mathematics
- 2015

We consider almost-primes of the form $f(p)$ where $f$ is an irreducible polynomial over $\mathbb Z$ and $p$ runs over primes. We improve a result of Richert for polynomials of degree at least $3$.… Expand

Almost-primes represented by quadratic polynomials

- Mathematics
- 2012

Let G(x) be an irreducible polynomial with integer coefficients. It is conjectured that the set {n ∈ N : G(n) is prime} is infinite for most G(x). If Pr denotes the set of squarefree positive… Expand

The least common multiple of consecutive quadratic progression terms

- Mathematics
- 2012

Let $k$ be an arbitrary given positive integer and let $f(x)\in {\mathbb Z}[x]$ be a quadratic polynomial with $a$ and $D$ as its leading coefficient and discriminant, respectively. Associated to the… Expand

Topologically slice knots of smooth concordance order two

- Mathematics
- 2012

The existence of topologically slice knots that are of infinite order in the knot concordance group followed from Freedman's work on topological surgery and Donaldson's gauge theoretic approach to… Expand

Sur un problème de Gelfond: la somme des chiffres des nombres premiers

- Mathematics
- 2010

L'objet de cet article est de repondre a une question posee par Gelfond en 1968 en montrant que la somme des chiffres s q (p) des nombres premiers p ecrits en base q ≥ 2 est equirepartie dans les… Expand

On the Liouville function at polynomial arguments

- Mathematics
- 2020

Let $\lambda$ denote the Liouville function. A problem posed by Chowla and by Cassaigne-Ferenczi-Mauduit-Rivat-Sarkozy asks to show that if $P(x)\in \mathbb{Z}[x]$, then the sequence $\lambda(P(n))$… Expand

On Consecutive 1’s in Continued Fractions Expansions of Square Roots of Prime Numbers

- Mathematics
- Experimental Mathematics
- 2019

In this note, we study the problem of existence of sequences of consecutive 1's in the periodic part of the continued fractions expansions of square roots of primes. We prove unconditionally that,… Expand

The Green-Tao theorem for Piatetski-Shapiro primes

- Mathematics
- 2019

Let $m\geq 3$. Suppose that $$ 1-2^{-2^{m^24^m}}<\gamma<1. $$ Then the set $$ \{p\text{ prime}:\, p=[n^{\frac1\gamma}]\text{ for some }n\in{\mathbb N}\} $$ contains infinitely many non-trivial… Expand

Spacing and A Large Sieve Type Inequality for Roots of a Cubic Congruence.

- Mathematics
- 2018

Motivated by a desire to understand the distribution of roots of cubic congruences, we re-derive a parametrization of roots $\nu \pmod m$ of $X^3 \equiv 2 \pmod m$ found by Hooley. Although this… Expand

#### References

SHOWING 1-10 OF 14 REFERENCES

On the greatest prime factor of a quadratic polynomial

- Mathematics
- 1967

as x ~ ~ , for which as for many other interesting results in the theory of numbers we are indebted to Chebyshev, has a t t racted the interest of several mathematicians. Revealed posthumously as… Expand

ON THE DISTRIBUTION OF ALMOST PRIMES IN AN INTERVAL

- Mathematics
- 1975

In this paper we shall prove that for a large positive number x there exist at least two
integers n in the interval x-x~(1/2)n≤x having at most two prime factors.

On some improvements of the Brun-Titchmarsh theorem, III

- Mathematics
- 1974

The aim of the present note is to give a version of large sieve extensions of the Brun– Titchmarsh theorem. This is in fact a rework of our old file left unpublished since early 1980’s which we… Expand

On the Brun-Titchmarsh theorem.

- Mathematics
- 1972

where π(χ\ α, k) denotes s is customary the number of primes not exceeding χ that are eongruent to a, modulo k. This theorem, which is now commonly known s the BrunTitchmarsh theorem, has… Expand

Selberg's sieve with weights

- Mathematics
- 1969

Let be a (finite) non-empty sequence of integers, and let K be a positive integer. The aim of the Brun-Selberg sieve is to obtain bounds for the “sifting function” where z ≥ 2 is a real number and

On the number of divisors of quadratic polynomials

- Mathematics
- 1963

A switch for a suspended railway vehicle having two elastic wheels, comprises four rails forming three paths one of which branches off into two other paths. A gap is bounded between the four rails.… Expand

A heuristic asymptotic formula concerning the distribution of prime numbers

- Mathematics
- 1962

Suppose fi, f2, -*, fk are polynomials in one variable with all coefficients integral and leading coefficients positive, their degrees being hi, h2, **. , hk respectively. Suppose each of these… Expand