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math.NT2025
Growth rates of sequences governed by the squarefree properties of its translates
Wouter van Doorn, Terence Tao
We answer several questions of Erdős regarding sequences of natural numbers whose translates intersect with the squarefree numbers in various specified ways. For instance…
math.NT2025★ 1 cited
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach
Terence Tao, Tim Trudgian, Andrew Yang
We obtain several new bounds on exponents of interest in analytic number theory, including four new exponent pairs, new zero density estimates for the Riemann zeta-function, and ne…