James Maynard

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20122026

most citedNew large value estimates for Dirichlet polynomials

4 citations · 8 across the 7 of their papers we have counts for

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math.NT2026

Counterexamples to the inhomogeneous Duffin-Schaeffer Conjecture

Manuel Hauke-Treuer, James Maynard, Andrew Pollington

The Duffin-Schaeffer Conjecture, proven in 2020, gives a zero-full dichotomy for the approximation of irrational numbers with reduced fractions for arbitrary approximation function…

math.NT2026

Exponential sums over primes

James Maynard, Mayank Pandey, Maksym Radziwiłł

Let $α = a / q + ε$ with $(a, q) = 1$ , $q \leq N^{1/2}$ and $∣ ε ∣ \leq 1/ (q N^{1/2})$ , and let $B := max (q, q N ∣ ε ∣)$ . We show that \[ \Bigl|\sum_{n<N}Λ(n)e(nα)\Bigr|\le N^{o(1)}\Bigl(\frac{N}{B^{1/2…