Xiannan Li

Conditional bounds for the least quadratic non-residue and related problems

This paper studies explicit and theoretical bounds for several interesting quantities in number theory, conditionally on the Generalized Riemann Hypothesis. Specifically, we improve the existing explicit bounds for the least quadratic non-residue and the least prime in an arithmetic progression. We also refine the classical conditional bounds of Littlewood for

The sixth moment of automorphic L-functions

L

Upper Bounds on L-Functions at the Edge of the Critical Strip

-functions at

The Riemann Zeta Function on Vertical Arithmetic Progressions

s=1

The smallest prime that does not split completely in a number field

. In particular, we derive explicit upper and lower bounds for

Lower Bounds for Small Fractional Moments of Dirichlet L-Functions

L(1,\chi)

A quadratic divisor problem and moments of the Riemann zeta-function

and

Almost prime triples and Chen's theorem

\zeta(1+it)

THE LEAST QUADRATIC NON-RESIDUE, VALUES OF L-FUNCTIONS AT s = 1, AND RELATED PROBLEMS

, and deduce explicit bounds for the class number of imaginary quadratic fields. Finally, we improve the best known theoretical bounds for the least quadratic non-residue, and more generally, the least

The 8th Moment of the Family of

k