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A family of deformations of the Riemann xi-function

Volume 157 / 2013

Masatoshi Suzuki Acta Arithmetica 157 (2013), 201-230 MSC: Primary 11M06; Secondary 11M41. DOI: 10.4064/aa157-3-1


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.


  • Masatoshi SuzukiDepartment of Mathematics
    Tokyo Institute of Technology
    2-12-1 Ookayama, Meguro-ku
    Tokyo 152-8551, Japan

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