Andriy Bondarenko

Large greatest common divisor sums and extreme values of the Riemann zeta function

It is shown that the maximum of

On Borsuk’s Conjecture for Two-Distance Sets

|\zeta(1/2+it)|

An inequality of Hardy–Littlewood type for Dirichlet polynomials

on the interval

Spherical Designs via Brouwer Fixed Point Theorem

T^{1/2}\le t \le T

Helson's problem for sums of a random multiplicative function

is at least

Pseudomoments of the Riemann zeta function

\exp\left((1/\sqrt{2}+o(1)) \sqrt{\log T \log\log\log T/\log\log T}\right)

Gál-type GCD sums beyond the critical line

. Our proof uses Soundararajans resonance method and a certain large GCD sum. The method of proof shows that the absolute constant

Non-existence of (76,30,8,14) strongly regular graph

A

Note on the Resonance Method for the Riemann Zeta Function

in the inequality \[ \sup_{1\le n_1<\cdots < n_N} \sum_{k,{\ell}=1}^N\frac{\gcd(n_k,n_{\ell})}{\sqrt{n_k n_{\ell}}} \ll N \exp\left(A\sqrt{\frac{\log N \log\log\log N}{\log\log N}}\right), \] established in a recent paper of ours, cannot be taken smaller than

There Is No Strongly Regular Graph with Parameters (460, 153, 32, 60)

1