A. Simonič

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math.NT2020

Some explicit and unconditional results on gaps between zeroes of the Riemann zeta-function

A. Simonič, T. Trudgian, C. L. Turnage-Butterbaugh

We make explicit an argument of Heath-Brown concerning large and small gaps between nontrivial zeroes of the Riemann zeta-function, $ζ (s)$ . In particular, we provide the first unco…

math.NT2020

On explicit estimates for $S (t)$ , $S_{1} (t)$ , and $ζ (1/2 + i t)$ under the Riemann Hypothesis

Aleksander Simonič

Assuming the Riemann Hypothesis, we provide explicit upper bounds for moduli of $S (t)$ , $S_{1} (t)$ , and $ζ (1/2 + i t)$ while comparing them with recently proven unco…

math.NT2019

On Littlewood's proof of the prime number theorem

Aleksander Simonič

In this note we examine Littlewood's proof of the prime number theorem. We show that this can be extended to provide an equivalence between the prime number theorem and the non-van…

Some explicit and unconditional results on gaps between zeroes of the Riemann zeta-function

On explicit estimates for S(t), S1​(t), and ζ(1/2+it) under the Riemann Hypothesis

On Littlewood's proof of the prime number theorem

On explicit estimates for $S (t)$ , $S_{1} (t)$ , and $ζ (1/2 + i t)$ under the Riemann Hypothesis