Room 509, Cosmology Building, NTU
(臺灣大學次震宇宙館 509研討室)
On Deligne’s Conjecture for Symmetric Fifth L-functions of Modular Forms
Shih-Yu Chen (National Tsing Hua University)
Abstract:
Given an elliptic newform
![](https://chart.googleapis.com/chart?cht=tx&chl=%24f%24&chf=bg,s,333333&chco=ffffff)
, we can associate the symmetric
![](https://chart.googleapis.com/chart?cht=tx&chl=%24n%24&chf=bg,s,333333&chco=ffffff)
-th power
![](https://chart.googleapis.com/chart?cht=tx&chl=%24L%24&chf=bg,s,333333&chco=ffffff)
-functions
![](https://chart.googleapis.com/chart?cht=tx&chl=%24L(s%2C%20Sym%5En(f))%24&chf=bg,s,333333&chco=ffffff)
for each
![](https://chart.googleapis.com/chart?cht=tx&chl=%24n%20%5Cgeq%201%24&chf=bg,s,333333&chco=ffffff)
. In 1977, Deligne’s proposed a conjecture on the algebraicity of critical values of
![](https://chart.googleapis.com/chart?cht=tx&chl=%24L(s%2C%20Sym%5En(f))%24&chf=bg,s,333333&chco=ffffff)
in terms of periods attached to
![](https://chart.googleapis.com/chart?cht=tx&chl=%24f%24&chf=bg,s,333333&chco=ffffff)
. The conjecture was considered by various authors when
![](https://chart.googleapis.com/chart?cht=tx&chl=%24n%20%3D%201%2C%202%2C%203%2C%204%2C%206%24&chf=bg,s,333333&chco=ffffff)
. In this talk, we will introduce a proof of the conjecture when
![](https://chart.googleapis.com/chart?cht=tx&chl=%24n%20%3D%205%24&chf=bg,s,333333&chco=ffffff)
.
JOIN WEBEX MEETING
Meeting number (access code): 2519 434 0700
Meeting password: HykvMTVH899 (49586884 from phones and video systems)