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5 papers
Twisted th moments of primitive Dirichlet -functions: beyond the diagonal
Siegfred Baluyot, Caroline L. Turnage-Butterbaugh
We study the family of Dirichlet -functions of all even primitive characters of conductor at most , where is a parameter tending to . For an arbitrary positive in…
Hilbert transforms and the equidistribution of zeros of polynomials
Emanuel Carneiro, Mithun Kumar Das, Alexandra Florea +5
We improve the current bounds for an inequality of Erdős and Turán from 1950 related to the discrepancy of angular equidistribution of the zeros of a given polynomial. Building upo…
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, . In particular, we provide the first unco…
A note on small gaps between zeros of the Riemann zeta-function
D. A. Goldston, C. L. Turnage-Butterbaugh
Assuming the Riemann Hypothesis, we improve on previous results by proving there are infinitely many zeros of the Riemann zeta-function whose differences are smaller than 0.50412 t…
Extremal primes of elliptic curves without complex multiplication
C. David, A. Gafni, A. Malik +2
Fix an elliptic curve E over Q. An extremal prime for E is a prime p of good reduction such that the number of rational points on E modulo p is maximal or minimal in relation to th…