九州大学 研究者情報
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基本情報 研究活動 教育活動 社会活動
翁 林(うぇん りん) データ更新日:2020.04.30

教授 /  数理学研究院 数学部門 数学部門


主な研究テーマ
数論特性曲線、数論Higgs束
キーワード:数論特性曲線、数論Higgs束
2019.01~2020.03.
Zeta Functions for Reductive Groups and Their Zeros
キーワード:Zeta Functions, Reductive Groups, Riemann Hypothesis
2000.12~2020.04.
Uniformity of zeta functions
キーワード:zeta 函数
2015.04~2020.03.
安定性と数論
キーワード:安定性、zeta 函数
2010.04~2015.03.
Geometric Arithmetic
キーワード:非可換類体論, 非可換ゼッタ関数, リーマン予想に関わる数論
1999.06.
Arithmetic Aspects of Moduli Spaces of Punctured Riemann Surfaces
キーワード:Weil-Petersson, Takhtajan-Zograf
2000.03.
Relative Bott-Chern Secondary Characteristic Classes and Arithmetic Grothendieck-Riemann-Roch Theorem for L.C.I. Morphisms
キーワード:Relative Bott-Chern Secondary Class, Grothendieck-Riemann-Roch Theorem
1990.06.
研究業績
主要著書
1. Lin WENG, Zeta Functions for Reductive Groups and Their Zeros, World Scientific, pp 528+xxvii, 2018.02, [URL], In this book, we develop a basic theory for new yet genuine zeta functions functions for number fields, establish the spacial uniformity of zeta functions on the equivalence of rank n non-abelian zeta functions and SL(n)-zeta functions, based on Siegel-Langland' theory of Eisenstein series. In particular, we confirm a central conjecture on "Parabolic Reduction, Stability and the Volumes". The key to this is an analytic version of the Mumford'S GIT correspondence between un-stable principle bundles and the parabolic subgroups of the associated reductive groups. This itself is based on an equivalence between Arthur's analytic truncation on the adelic spaces and the geo-arithmetic truncation of stability on principal bundles. Finally, we prove the Riemann hypothesis for our zeta functions. The book consists of 7 parts: Part 1 Non-Abelian Zeta Function Part 2 Rank 2 Zeta Functions Part 3 Eisensetin Periods and Multiple Zeta Functions Part 4 Zeta Functions for Reductive Groups Part 5 Algebraic and Analytic Structures and Riemann Hypothesis Part 6 Geometric Structures and Riemann Hypothesis Appendices (with K. Sugahara) Five Essays On Arithmetic Cohomology.
主要原著論文
1. #Lin WENG(九大の教員), 他@Don Zagier, Higher-rank zeta functions and $SL_n$-zeta functions for curves, 米国科学アカデミー紀要(PNAS), PNAS March 24, 2020 117 (12), PNAS March 24, 2020 117 (12), 6398-6408, 2020.03, [URL], In earlier papers L.Weng introduced two sequences of higher-rank zeta functions associated to a smooth projective curve over a finite
field, both of them generalizing the Artin zeta function of the curve. One of these zeta functions is defined geometrically in terms of
semistable vector bundles of rank n over the curve, and the other one group-theoretically in terms of certain periods associated to the
curve and to a split reductive group G and its maximal parabolic subgroup P. It was conjectured that these two zeta functions coincide
in the special case when G = $SL_n$ and $P$ is the parabolic subgroup consisting of matrices whose final row vanishes except for its last
entry. In this paper we prove this equality by giving an explicit inductive calculation of the group-theoretically defined zeta functions in
terms of the original Artin zeta function (corresponding to n = 1) and then verifying that the result obtained agrees with the inductive
determination of the geometrically defined zeta functions found by Sergey Mozgovoy and Markus Reineke in 2014..
2. L. Weng, D. Zagier, Higher rank zeta functions for elliptic curves, 米国科学アカデミー紀要(PNAS), PNAS March 3, 2020 117 (9), PNAS March 3, 2020 117 (9), 4546-4558, 2020.02, [URL], The rank n non-abelian zeta functions for curves over finite fields was defined by the first author in 2005,
using moduli stacks of rank n semi-stable vector bundles on curves. These zeta functions satisfy the standard
zeta properties such as the rationality, the functional equation and are conjectured to satisfy the Riemann Hypothesis.
In particular, when n=1, these zeta functions coincide with the famous Artin zeta functions.
In this paper, we prove the Riemann hypothesis for non-abelian zeta functions of elliptic curves..
主要総説, 論評, 解説, 書評, 報告書等
主要学会発表等
学会活動
学会大会・会議・シンポジウム等における役割
2014.06.30~2014.07.01, Bundles over Surfaces and Eisenstein Periods for Loop Groups, 座長(Chairmanship).
2013.05.01~2013.05.01, First Kyushu Joint Seminar.
2013.04.26~2013.04.28, Symposium on Automorphic Functions and Arithmetic Geometry: One for Prof. L. Lafforgue's visit.
2012.10.19~2012.10.21, Symposium on Arithmetic Geometry.
2012.06.01~2012.06.02, Symposium on Arithmetic & Geometry.
2011.04.21~2011.04.23, Workshop on L-Functions.
2007.09~2019.06.16, Algebraic and Arithmetic Structures of Moduli Spaces.
2006.02, Conference on L-Functions.
2005.03, Arithmetic Geometry and Number Theory.
2004.05, Towards IC Stability.
2014.06.30~2014.07.01, Bundles over Surfaces and Eisenstein Periods for Loop Groups, 主催.
2013.04.26~2013.04.28, Symposium on Automorphic Functions and Arithmetic Geometry: One for Prof. L. Lafforgue's visit, 主催.
2012.10.19~2012.10.21, Symposium on Arithmetic Geometry, 主催.
2012.06.01~2012.06.02, Symposium on Arithmetic & Geometry, 主催.
2011.04.21~2011.04.23, Workshop on L-Functions, Organizer.
2007.09, Algebraic and Arithmetic Aspects of Moduli Spaces, Organizer.
2006.02, Conference on L-Functions, Organizer.
2005.03, Arithmetic Geometry and Number Theory, Organizer.
2004.01, Towards IC Stability, Organizer.

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