Quanli Shen

I will discuss the fourth moment of quadratic Dirichlet L-functions where we prove an asymptotic formula with four main terms unconditionally. Previously, the asymptotic formula was established with the leading main term under generalized Riemann...

We obtain the asymptotic formula with an error term O ( X 1 2 + ε ) O ( X 1 2 + ε ) for the smoothed first moment of quadratic twists of modular L L -functions. The argument is largely based on a recursive method of Young (Acta Arith. 138(1):73–99...

The ternary Goldbach problem stated that every odd integer greater than 5 can be written as sums of three primes. This was proved by Vinogradov for all sufficiently large odd integers and completely proved by Helfgott. On the other hand, by using...

In this talk, I will talk about the fourth moment of quadratic Dirichlet L-functions. Under the generalized Riemann hypothesis, we showed an asymptotic formula for the fourth moment. Unconditionally, we established a precise lower bound.