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