26 citations · 82 across the 19 of their papers we have counts for
22 papers
Siegel zeros and small gaps between zeros of the Riemann zeta function
Andriy Bondarenko, Winston Heap
On assuming the Riemann Hypothesis, we show that Siegel zeros imply the existence of gaps between the zeros of the Riemann zeta function less than 1/2 the normalised length. Specif…
An Analogue of the Dedekind Eta Function for Hecke Groups
Debmalya Basak, Dorian Goldfeld, Winston Heap +2
Let be a fundamental discriminant of a real quadratic field. We construct an analogue of the classical Dedekind eta function for the Hecke group .…
The fourth moment of the Hurwitz zeta function
Winston Heap, Anurag Sahay
We prove a sharp upper bound for the fourth moment of the Hurwitz zeta function on the critical line when the shift parameter is irrational and of irrationality expone…
Simultaneous extreme values of zeta and L-functions
Winston Heap, Junxian Li
We show that distinct primitive L-functions can achieve extreme values simultaneously on the critical line. Our proof uses a modification of the resonance method and can be applied…
A dichotomy for extreme values of zeta and Dirichlet L-functions
Andriy Bondarenko, Pranendu Darbar, Markus Valås Hagen +2
We exhibit large values of the Dedekind zeta function of a cyclotomic field on the critical line. This implies a dichotomy whereby one either has improved lower bounds for the maxi…
Conditional mean values of long Dirichlet polynomials
Winston Heap
Conditionally on the Riemann hypothesis we prove asymptotic formulae for mean values of various long Dirichlet polynomials involving the von Mangoldt function. Our results avoid th…