Báo cáo viên: Ngô Trung Hiếu (VIASM)
**Thời gian**: 9h, Thứ 4, 10/4/2019
**Địa điểm**: Phòng 611-612, Tòa A6, Viện Toán học
**Tóm tắt**:A basic question in number theory is to understand the distribution of values of L-functions inside the critical strip. In this talk we will address the central values of Dirichlet L-functions.
A classical theorem of Iwaniec and Sarnak asserts that at least one-third of the central values of Dirichlet L-functions do not vanish when the conductor approaches infinity. We will describe a strengthening which says that when the conductor is a prime power and the Dirichlet L-functions are partitioned according to a natural Galois action, the one-third nonvanishing proportion holds within each Galois orbit. We will present a barrier-breaking mollifier method, improving the nonvanishing proportion to three-eighth when the conductor takes values in the sequence of prime numbers. This is joint work with Rizwanur Khan and Djordje Milicevic. |