Work

Local average in the hyperbolic sphere problem

Year: 2026

Type: article

Abstract: We consider a local average in the hyperbolic lattice point counting problem for the Picard group Γ \Gamma acting on the three-dimensional hyperbolic space. Compared to the pointwise case, we improve the bounds on the remainder in the counting, conditionally on a quantum variance estimate for Maass cusp forms attached to Γ \Gamma . We also use bounds on a spectral exponential sum over the Laplace eigenvalues for Γ \Gamma , which has been studied in the context of the prime geodesic theorem and for which unconditional bounds are known.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17574

Authors: Giacomo Cherubini, Christos Katsivelos

Institutions: Istituto Nazionale di Alta Matematica Francesco Severi, Sapienza University of Rome, University of Patras

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Hellenic Foundation for Research and Innovation

Award: Προβλήματα απαρίθμησης και ισοκατανομής στην αυτομορφική θεωρία αριθμών