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Title	Zeta polynomials for modular forms
Creator	Ono, Ken
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2016-09-29T09:00
Description	The speaker will discuss recent work on Manin's theory of zeta polynomials for modular forms. He will describe recent results which confirm Manin's speculation that there is such a theory which arises from periods of newforms. More precisely, for each even weight $k>2$ newform $f$ the speaker will describe a canonical polynomial $Z_f (s)$ which satisfies a functional equation of the form $Z_f (s) = Z_f (1 - s)$, and also satisfies the Riemann Hypothesis: if $Z_f (\rho) = 0$, then $Re(\rho) = 1/2$. This zeta function is arithmetic in nature in that it encodes the mo- ments of the critical values of $L(f, s)$. This work builds on earlier results of many people on period polynomials of modular forms. This is joint work with Seokho Jin, Wenjun Ma, Larry Rolen, Kannan Soundararajan, and Florian Sprung.
Extent	50 minutes
Subject	Mathematics Number theory Algebraic geometry
Geographic Location	Banff (Alta.)
Type	Moving Image
FileFormat	video/mp4
Language	eng
Notes	Author affiliation: Emory University
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2017-03-30
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0343419
URI	http://hdl.handle.net/2429/61065
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
AggregatedSourceRepository	DSpace

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