A family of deformations of the Riemann xi-function
Volume 157 / 2013
Acta Arithmetica 157 (2013), 201-230
MSC: Primary 11M06; Secondary 11M41.
DOI: 10.4064/aa157-3-1
Abstract
We introduce a family of deformations of the Riemann xi-function endowed with two continuous parameters. We show that it has rich analytic structure and that its conjectural (mild) zero-free region for some fixed parameter is a sufficient condition for the Riemann hypothesis to hold for the Riemann zeta function.
