2 citations · 3 across the 8 of their papers we have counts for
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Four consecutive primitive elements in a finite field
Tamiru Jarso, Tim Trudgian
For an odd prime power, we prove that there are always four consecutive primitive elements in the finite field when .
Explicit lower bounds on
Michael J. Mossinghoff, Valeriia V. Starichkova, Timothy S. Trudgian
Let denote a primitive, non-quadratic Dirichlet character with conductor , and let denote its associated Dirichlet -function. We show that $|L(1, χ)| \geq 1/(9.…
The mean square of the error term in the prime number theorem
Richard P. Brent, David J. Platt, Timothy S. Trudgian
We show that, on the Riemann hypothesis, , where This proves (and improves on) a claim by Pintz fro…
Oscillations in weighted arithmetic sums
Michael J. Mossinghoff, Timothy S. Trudgian
We examine oscillations in a number of sums of arithmetic functions involving , the total number of prime factors of , and , the number of distinct prime factors of…
The size of oscillations in the Goldbach conjecture
Michael J. Mossinghoff, Timothy S. Trudgian
Let , where is the von Mangoldt function. The function is often studied in connection with Goldbach's conjecture. On the Riemann hyp…
The Riemann hypothesis is true up to
Dave Platt, Tim Trudgian
We verify numerically, in a rigorous way using interval arithmetic, that the Riemann hypothesis is true up to height . That is, all zeroes of the Riemann zet…