A. J. Irving

activity

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 2013Show all

3 papers · 1 filter

math.NT2013★ 2 cited

Cubic polynomials represented by norm forms

A. J. Irving

We show that for an irreducible cubic $f \in Z [x]$ and a full norm form $N (x_{1}, \dots, x_{k})$ for a number field $K / Q$ satisfying certain hypotheses the variety…

math.NT2013★ 4 cited

Diophantine Approximation with Products of Two Primes

A. J. Irving

We show that for any irrational $α$ and any $τ < 8/23$ there are infinitely many $n$ which are the product of two primes for which $∥ n α ∥ \leq n^{- τ} .$ We also show that for all su…

math.NT2013★ 1 cited

Average Bounds for Kloosterman Sums Over Primes

A. J. Irving

We prove two estimates for averages of sums of Kloosterman fractions over primes. The first of these improves previous results of Fouvry-Shparlinski and Baker.