2
votes
2answers
228 views

Weyl law for arithmetic Fuchsian groups known?

For congruence subgroups of $PSL(2,\mathbb{Z})$, the Weyl law for the eigenvalues of Maass cusp forms had been proven by Selberg. How is the status of such a Weyl law for eigenvalues of Maass cusp ...
5
votes
3answers
452 views

Multiplicity one conjecture

I recently became interested in Maass cusp forms and heared people mentioning a "multiplicity one conjecture". As far as I understood it, it says that the dimension of the space of Maass cusp form for ...
1
vote
0answers
169 views

Norm related to diophantine approximation?

I'm trying to read this paper: http://www.springerlink.com/content/g0046660260825x3/ or http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.20.1813&rep=rep1&type=pdf But I don't ...
5
votes
1answer
1k views

The Guinand-Weil explicit formula without entire function theory

I'll admit from the outset that this question is slightly vague. The actual question appears at the end of the post. The explicit formula of Guinand and Weil can be written in the following way: For ...
27
votes
3answers
2k views

Perron-Frobenius “inverse eigenvalue problem”

The Perron-Frobenius theorem says that the largest eigenvalue of a positive real matrix (all entries positive) is real. Moreover, that eigenvalue has a positive eigenvector, and it is the only ...
4
votes
0answers
461 views

An inverse eigenvalue problem on Jacobi matrices

I am interested in trying to design a Hermitian Jacobi (tridiagonal) matrix $H$ that has specific properties. The basic property, which is simple enough to construct, is that for an $N\times N$ matrix ...
9
votes
3answers
1k views

Number Theory and Geometry/Several Complex Variables

This is a question for all you number theorists out there...based on my skimming of number theory textbooks and survey articles, it seems like most of the applications of geometry and complex ...