A. J. Irving

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20132015

most citedAlmost-prime values of polynomials at prime arguments

7 citations · 17 across the 9 of their papers we have counts for

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Showing 2014 · math.NTShow all

4 papers · 2 filters

math.NT2014

The largest prime factor of $X^{3} + 2$

A. J. Irving

Improving on a theorem of Heath-Brown, we show that if $X$ is sufficiently large then a positive proportion of the values ${n^{3} + 2 : n \in (X, 2 X]}$ have a prime factor larger than $X…

math.NT2014★ 7 cited

Almost-prime values of polynomials at prime arguments

A. J. Irving

We consider almost-primes of the form $f (p)$ where $f$ is an irreducible polynomial over $Z$ and $p$ runs over primes. We improve a result of Richert for polynomials of deg…

math.NT2014

The divisor function in arithmetic progressions to smooth moduli

A. J. Irving

By using the $q$ -analogue of van der Corput's method we study the divisor function in an arithmetic progression to modulus $q$ . We show that the expected asymptotic formula holds f…

math.NT2014

Almost prime values of binary forms with one prime variable

A. J. Irving

By establishing an improved level of distribution we study almost primes of the form $f (p, n)$ where $f$ is an irreducible binary form over $Z$ .

The largest prime factor of X3+2

Almost-prime values of polynomials at prime arguments

The divisor function in arithmetic progressions to smooth moduli

Almost prime values of binary forms with one prime variable

The largest prime factor of $X^{3} + 2$