PreprintarXiv licencearXiv
Surfaces Associated to Zeros of Automorphic L-functions
Abstract
Assuming the Riemann Hypothesis, Montgomery established results concerning pair correlation of zeros of the Riemann zeta function. Rudnick and Sarnak extended these results to automorphic L-functions and all level correlations. We discover additional geometric structures associated to the zeros of automorphic L-functions. In the case of pair correlation, these structures form certain surfaces which display Gaussian behavior. For triple correlation, these structures exhibit Laplace and Chi-squared distributions, revealing an unexpected phase transition.
Related
- Bilinear maximal functions associated with some degenerate surfaces on the Heisenberg group
- Vertex operator algebra bundles on Riemann surfaces of higher genus and automorphic forms for Fuchsian groups
- K-Moduli Wall Crossing and Automorphic Forms for the Moduli Space of Rational Elliptic Surfaces
- Lower Bounds for Localised Moments of Automorphic L-functions
- Zero density estimates for GL2 automorphic L-functions
BibTeX
@misc{basak2026surfaces,
title = {{Surfaces Associated to Zeros of Automorphic $L$-functions}},
author = {Debmalya Basak and Cruz Castillo and Alexandru Zaharescu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26575},
eprint = {2610.26575},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26575},
}
RIS
TY - UNPB
TI - Surfaces Associated to Zeros of Automorphic L-functions
AU - Debmalya Basak
AU - Cruz Castillo
AU - Alexandru Zaharescu
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26575
UR - https://arxiv.org/abs/2610.26575
AB - Assuming the Riemann Hypothesis, Montgomery established results concerning pair correlation of zeros of the Riemann zeta function. Rudnick and Sarnak extended these results to automorphic L-functions and all level correlations. We discover additional geometric structures associated to the zeros of automorphic L-functions. In the case of pair correlation, these structures form certain surfaces which display Gaussian behavior. For triple correlation, these structures exhibit Laplace and Chi-squared distributions, revealing an unexpected phase transition.
ER -