Author

Mayank Pandey

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Preprint Oct 2026

The sixth moment of the Riemann zeta function

We prove new large value estimates for the Riemann zeta function on the critical line. For instance, we improve the upper bound on the measure of $t\in [T, 2T]$ with $|\zeta(1/2 + it)| \geq T^{1/8}$ for the first time since Hardy-Littlewood (1923). Our results imply improved upper bounds on the $k$-th moment of zeta fo...

Alexandre de Faveri, Mayank Pandey · 0 citations

Preprint Aug 2026

Exponential sums over primes

Let $\alpha=a/q+\epsilon$ with $(a,q)=1$, $q\le N^{1/2}$ and $|\epsilon|\le 1/(qN^{1/2})$, and let $B:=\max(q,qN|\epsilon|)$. We show that \[ \Bigl|\sum_{n<N}\Lambda(n)e(n\alpha)\Bigr|\le N^{o(1)}\Bigl(\frac{N}{B^{1/2}}+N^{19/24}\Bigr). \] This improves on the classical bound of Vinogradov from 1937, which has $N^{4/5}...

James Maynard, Mayank Pandey, Maksym Radziwiłł · 0 citations