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Zeta Polynomials for Modular Forms

Dr. Ken Ono, Emory University

Zeta Polynomials for Modular Forms

3:30 pm, Friday, February 24, TUC 244

In his tribute to Jean-Pierre Serre, Yuri Manin made speculations about his theory of “zeta-polynomials,” polynomials which are expected to satisfy the Riemann Hypothesis along with a host of features that are associated to Riemann’s zeta-function. In particular, he presented numerics which strongly suggested the existence of such a theory arising from numbers called “periods of modular forms.” The speaker and his collaborators have developed these speculations into a theory, and has proved the resulting conjectures. This lecture will begin with a survey of Riemann’s zeta-function, and will conclude with the new work. In particular, a proof of the Riemann Hypothesis for periods will be presented (Note. The famous Riemann Hypothesis remains open.)

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