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math.NT2026
Zero-free regions inspired by work of Heath-Brown
Chiara Bellotti, Tim Trudgian, Andrew Yang
We prove a new explicit zero-free region for the Riemann zeta-function, drawing substantially on Heath-Brown's seminal work on Linnik's constant. Using these ideas we are able to p…
math.NT2024
Explicit bounds for the Riemann zeta-function on the 1-line
Ghaith A. Hiary, Nicol Leong, Andrew Yang
Explicit estimates for the Riemann zeta-function on the -line are derived using various methods, in particular van der Corput lemmas of high order and a theorem of Borel and Car…
math.NT2024
Toward optimal exponent pairs
Timothy S. Trudgian, Andrew Yang
We quantify the set of known exponent pairs and develop a framework to compute the optimal exponent pair for an arbitrary objective function. Applying this methodology,…