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Explicit estimates for the Riemann zeta-function on the $1$-line are derived using various methods, in particular van der Corput lemmas of high order and a theorem of Borel and Carath\'{e}odory.
Comment: 31 pages
Comment: 31 pages
Externí odkaz:
http://arxiv.org/abs/2306.13289
Autor:
Trudgian, Timothy S., Yang, Andrew
We quantify the set of known exponent pairs $(k, \ell)$ and develop a framework to compute the optimal exponent pair for an arbitrary objective function. Applying this methodology, we make progress on several open problems, including bounds of the Ri
Externí odkaz:
http://arxiv.org/abs/2306.05599
Autor:
Patel, Dhir, Yang, Andrew
In this article we prove an explicit sub-Weyl bound for the Riemann zeta function $\zeta(s)$ on the critical line $s = 1/2 + it$. In particular, we show that $|\zeta(1/2 + it)| \le 66.7\, t^{27/164}$ for $t \ge 3$. Combined, our results form the shar
Externí odkaz:
http://arxiv.org/abs/2302.13444
An explicit subconvex bound for the Riemann zeta function $\zeta(s)$ on the critical line $s=1/2+it$ is proved. Previous subconvex bounds relied on an incorrect version of the Kusmin-Landau lemma. After accounting for the needed correction in that le
Externí odkaz:
http://arxiv.org/abs/2207.02366
Autor:
Patel, Dhir
In this paper we provide an explicit bound for $|\zeta(1+it)|$ in the form of $|\zeta(1+it)|\leq \min\left(\log t, \frac{1}{2}\log t+1.93, \frac{1}{5}\log t+44.02 \right)$. This improves on the current best-known explicit bound of $|\zeta(1+it)|\leq
Externí odkaz:
http://arxiv.org/abs/2009.00769
Autor:
Bourgain, Jean
We establish a new decoupling inequality for curves in the spirit of [B-D1], [B-D2] which implies a new mean value theorem for certain exponential sums crucial to the Bombieri-Iwaniec method as developed further in [H]. In particular, this leads to a
Externí odkaz:
http://arxiv.org/abs/1408.5794
Autor:
Trudgian, Timothy S., Yang, Andrew
We quantify the set of known exponent pairs $(k, \ell)$ and develop a framework to compute the optimal exponent pair for an arbitrary objective function. Applying this methodology, we make progress on several open problems, including bounds of the Ri
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::41116f4fa1e7610ead6861bf5d25a4c9
Autor:
Jean Bourgain
We establish a new decoupling inequality for curves in the spirit of [B-D1], [B-D2] which implies a new mean value theorem for certain exponential sums crucial to the Bombieri-Iwaniec method as developed further in [H]. In particular, this leads to a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d4720713f015f9bb5ad2c5b4ff7b6da0
http://arxiv.org/abs/1408.5794
http://arxiv.org/abs/1408.5794