TY - UNPB

T1 - Large sets of consecutive Maass forms and fluctuations in the Weyl remainder

AU - Then, Holger

PY - 2012/12/13

Y1 - 2012/12/13

N2 - We explore an algorithm which systematically finds all discrete
eigenvalues of an analytic eigenvalue problem. The algorithm is more
simple and elementary as could be expected before. It consists of
Hejhal's identity, linearisation, and Turing bounds. Using the
algorithm, we compute more than one hundredsixty thousand consecutive
eigenvalues of the Laplacian on the modular surface, and investigate the
asymptotic and statistic properties of the fluctuations in the Weyl
remainder. We summarize the findings in two conjectures. One is on the
maximum size of the Weyl remainder, and the other is on the distribution
of a suitably scaled version of the Weyl remainder.

AB - We explore an algorithm which systematically finds all discrete
eigenvalues of an analytic eigenvalue problem. The algorithm is more
simple and elementary as could be expected before. It consists of
Hejhal's identity, linearisation, and Turing bounds. Using the
algorithm, we compute more than one hundredsixty thousand consecutive
eigenvalues of the Laplacian on the modular surface, and investigate the
asymptotic and statistic properties of the fluctuations in the Weyl
remainder. We summarize the findings in two conjectures. One is on the
maximum size of the Weyl remainder, and the other is on the distribution
of a suitably scaled version of the Weyl remainder.

KW - Mathematics - Number Theory

KW - Mathematical Physics

KW - 65N25

KW - 11N45 (primary)

KW - 11F41

KW - 11Y16

KW - 65-05 (secondary)

UR - https://arxiv.org/abs/1212.3149

M3 - Working paper and Preprints

BT - Large sets of consecutive Maass forms and fluctuations in the Weyl remainder

ER -