3 papers
math.CA2026
On the optimal constant in the Montgomery-Vaughan weighted Hilbert inequality
Brad Rodgers
We give a proof that the optimal constant in the weighted Hilbert inequality is strictly greater than , answering in the negative a question asked by Montgomery and Vaughan. The…
math.NT2020
Sums of singular series and primes in short intervals in algebraic number fields
Vivian Kuperberg, Brad Rodgers, Edva Roditty-Gershon
Gross and Smith have put forward generalizations of Hardy - Littlewood twin prime conjectures for algebraic number fields. We estimate the behavior of sums of a singular series tha…
math.NT2019
Higher Correlations and the Alternative Hypothesis
Jeffrey C. Lagarias, Brad Rodgers
The Alternative Hypothesis concerns a hypothetical and unlikely picture of how zeros of the Riemann zeta function are spaced which one would like to rule out. In the Alternative Hy…