6 papers
A decades-long breakthrough in zero-density estimates and primes in short intervals
Caroline L. Turnage-Butterbaugh
The Riemann Hypothesis (RH) asserts that every nontrivial zero of the Riemann zeta-function has real part equal to . A zero-density theorem provides evidence towards RH by bou…
A guide to Tauberian theorems for arithmetic applications
Lillian B. Pierce, Caroline L. Turnage-Butterbaugh, Asif Zaman
A Tauberian theorem deduces an asymptotic for the partial sums of a sequence of non-negative real numbers from analytic properties of an associated Dirichlet series. Tauberian theo…
Critical Zeros and Unconditional Mean Value Theorems for twisted and -functions
Brian Conrey, Chung-Hang Kwan, Yongxiao Lin +1
Let be a cuspidal automorphic representation of . In this paper, we use Levinson's method to prove that, as , at le…
Pair Correlation of Zeros of the Riemann Zeta Function I: Proportions of Simple Zeros and Critical Zeros
Siegfred Alan C. Baluyot, Daniel Alan Goldston, Ade Irma Suriajaya +1
Assuming the Riemann Hypothesis (RH), Montgomery proved a theorem in 1973 concerning the pair correlation of zeros of the Riemann zeta-function and applied this to prove that at le…
Short mollifiers of the Riemann zeta-function
J. Brian Conrey, David W. Farmer, Chung-Hang Kwan +2
We apply the calculus of variations to construct a new sequence of linear combinations of derivatives of the Riemann -function adapted to Levinson's method, which yield a posit…
The Alternative Hypothesis for Zeros of the Riemann Zeta-Function
Siegfred Alan C. Baluyot, Daniel Alan Goldston, Ade Irma Suriajaya +1
In 2016, the first-named author introduced a formulation of the Alternative Hypothesis that assumes that consecutive zeros of the Riemann zeta-function are spaced at multiples of h…