arXiv subjects

Jimi Lee Truelsen

Publications and source records attributed to Jimi Lee Truelsen.

2 recordsLinked to original sources

arXiv2009

Divisor problems and the pair correlation for the fractional parts of $n^2α$

Z. Rudnick and P. Sarnak have proved that the pair correlation for the fractional parts of $n^2 α$ is Poissonian for almost all $α$. However, they were not able to find a specific $α$ for which it holds. We show that the problem is related to the problem of determining the number of $(a,b,r) \in \N^3$ such that $a \le M$, $b \le N$, $r \le K$ and $p ab \equiv r (q)$ for $p$ and $q$ coprime. With suitable assumptions on the relative size of $K$, $M$, $N$ and $q$ one should expect there to be $KMN/q$ such triples asymptotically and we will show that this holds on average.

math.NT↗

arXiv2008

Quantum Unique Ergodicity for Eisenstein Series on the Hilbert Modular Group over a Totally Real Field

W. Luo and P. Sarnak have proved the quantum unique ergodicity property for Eisenstein series on $\rm{PSL}(2,\mathbb{Z}) \backslash H$. We extend their result to Eisenstein series on $\rm{PSL}(2,O) \backslash H^n$, where $O$ is the ring of integers in a totally real field of degree $n$ over $Q$ with narrow class number one, using the Eisenstein series considered by I. Efrat. We also give an expository treatment of the theory of Hecke operators on non-holomorphic Hilbert modular forms.

math.NT↗