4 papers
An arithmetic formula for certain coefficients of the Euler product of Hecke polynomials
Xian-Jin Li
In 1997 the author found a criterion for the Riemann hypothesis for the Riemann zeta function, involving the nonnegativity of certain coefficients associated with the Riemann zeta…
On the trace of Hecke operators for Maass forms for congruence subgroups II
Xian-Jin Li
Let E_lambda be the Hilbert space spanned by the eigenfunctions of the non-Euclidean Laplacian associated with a positive discrete eigenvalue lambda. In this paper, the trace of He…
On the trace of Hecke Operators for Maass forms for congruence subgroups
J. Brian Conrey, Xian-Jin Li
Let E_lambda be a Hilbert space, whose elements are functions spanned by the eigenfunctions of the Laplace-Beltrami operator associated with an eigenvalue lambda>0. The norm of ele…
A note on some positivity conditions related to zeta- and L-functions
J. Brian Conrey, Xian-Jin Li
L. de Branges proposed an approach to the Riemann hypothesis using certain positivity conditions. In this paper, the authors examine this approach and indicate its difficulty.