The limit points of the bass notes of arithmetic hyperbolic surfaces

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(Submitted on 1 Mar 2024 (v1), last revised 2 Apr 2024 (this version, v2))

Abstract: We prove that the limit points of the bass notes of arithmetic hyperbolic surfaces are the interval $\left[0,\frac{1}{4}\right]$.

Comments:	32 pages, 2 Figures, presentation polished in current version
Subjects:	Number Theory (math.NT); Analysis of PDEs (math.AP); Differential Geometry (math.DG); Probability (math.PR); Spectral Theory (math.SP)
MSC classes:	58J50, 05C80, 05C50
Cite as:	arXiv:2403.00928 [math.NT]
	(or arXiv:2403.00928v2 [math.NT] for this version)

From: Michael Magee [view email]
[v1] Fri, 1 Mar 2024 19:16:58 GMT (103kb,D)
[v2] Tue, 2 Apr 2024 20:08:15 GMT (104kb,D)