6 citations · 14 across the 11 of their papers we have counts for
11 papers
A Hilbert-Schmidt integral operator and the Weil distribution
Xian-Jin Li
In this paper, a positive operator is given. It is shown that the product of this positive operator and the convolution operator is a trace class Hilbert-Schmidt integral operator…
On the spectrum of a differential operator on a Hilbert-Pólya space
Xian-Jin Li
In this paper we study the spectrum of a fundamental differential operator on a Hilbert-Pólya space. A number is an eigenvalue of this differential operator if and only if it is a…
A proof of the Riemann hypothesis
Xian-Jin Li
In this paper we study traces of an integral operator on two orthogonal subspaces of a space. One of the two traces is shown to be zero. Also, we prove that the trace of the…
On exceptional eigenvalues of the Laplacian for
Xian-Jin Li
An explicit Dirichlet series is obtained, which represents an analytic function of in the half-plane except for having simple poles at points that correspond…
A note on zeros of -series of elliptic curves
Xian-Jin Li
In this note we study an analogy between a positive definite quadratic form for elliptic curves over finite fields and a positive definite quadratic form for elliptic curves over t…
An explicit formula for Hecke -functions
Xian-Jin Li
In this paper an explicit formula is given for a sequence of numbers. The positivity of this sequence of numbers implies that zeros in the critical strip of the Euler product of He…