KIAS Intensive Lecture Series-Number TheoryJan, 7 ~ 8, 2014, KIAS 4fl. Seminar Room |
Abstracts | Home > Abstracts |
kentaro Ihara
Title 1: Introduction to multiple zeta values--overview
Abstract of talk 1: In this talk, I introduce what are multiple zeta values (MZVs) and explain basic properties of them such as iterated integral expressions, shuffle/harmonic product, and several linear relations among them. Also I explain the structure of the algebra of MZVs and introduce related results.
Title 2 and 3: On multiple L-function of cusp forms I and II
Abstracts of talk 2 and 3: In these talks, I introduce the multiple L-function associated to elliptic cusp forms and discuss the property of special values. First I'll show an expression of the multiple L-function in terms of an iterated integral of cusp forms and state a result on the structure of the algebra generated by special values of multiple L-function. The result is an analogue of that in the theory of multiple zeta values.
Min Lee
Title: Shifted Multiple Dirichlet series and applicationsAbstract: In these three lectures, we introduce the shifted multiple Dirichlet series and study their analytic behaviors. The meromorphic continuation of these series is used to obtain a second moment formula for the L-series of holomorphic cusp forms.
1. Introduction: motivation and definitions2. Analytic properties of the shifted multiple Dirichlet series3. Applications to moments of L-functions
The main references are (on arXiv)Multiple Dirichlet series and shifted convolutions, Jeff Hoffstein and Thomas Hulse Second moments and simultaneous non-vanishing of GL(2) automorphic L-series, Jeff Hoffstein and Min Lee
Haesang Sun
Title : Modular symbol and related topicsAbstract : I am going to explain the basic definition and properties of modular symbols including its relation with continued fraction. Several topics are also going to be presented including the special values of modular L-function in the context of modular symbol. The level of contents will be quite elementary except last 10 to 15 minutes of the second lecture.