J. Maynard

activity

20182022

most citedPrimes in arithmetic progressions to large moduli II: Well-factorable estimates

4 citations · 14 across the 9 of their papers we have counts for

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math.NT2022

On the largest prime factor of quartic polynomial values: the cyclic and dihedral cases

Cécile Dartyge, James Maynard

Let $P (X) \in Z [X]$ be an irreducible, monic, quartic polynomial with cyclic or dihedral Galois group. We prove that there exists a constant $c_{P} > 0$ such that for a positive…

math.NT2020

Simultaneous small fractional parts of polynomials

James Maynard

Let $f_{1}, \dots, f_{k} \in R [X]$ be polynomials of degree at most $d$ with $f_{1} (0) = \dots = f_{k} (0) = 0$ . We show that there is an integer $n < x$ such that the fractional parts $\|f_i(…

math.NT2020

Metric theory of Weyl sums

Changhao Chen, Bryce Kerr, James Maynard +1

We prove that there exist positive constants $C$ and $c$ such that for any integer $d \geq 2$ the set of $x \in [0, 1)^{d}$ satisfying $$ cN^{1/2}\le \left|\sum^N_{n=1}\exp\le…

math.NT2020★ 2 cited

A new upper bound for sets with no square differences

Thomas F. Bloom, James Maynard

We show that if $A \subset {1, \dots, N}$ has no solutions to $a - b = n^{2}$ with $a, b \in A$ and $n \geq 1$ then \[|A|\ll \frac{N}{(\log N)^{c\log\log \log N}}\] for some absolute consta…

math.NT2020★ 1 cited

Primes in arithmetic progressions to large moduli III: Uniform residue classes

James Maynard

We prove new mean value theorems for primes in arithmetic progressions to moduli larger than $x^{1/2}$ , extending the Bombieri-Vinogradov theorem to moduli of size $x^{1/2 + δ}$ whic…

math.NT2020★ 4 cited

Primes in arithmetic progressions to large moduli II: Well-factorable estimates

James Maynard

We establish new mean value theorems for primes of size $x$ in arithmetic progressions to moduli as large as $x^{3/5 - ε}$ when summed with suitably well-factorable weights. This ext…