Refinements to the Kuznetsov Formula for Laplace-Beltrami Operators
Abstract
Wyman and Xi (2023) proved a Kuznetsov-type theorem for the submanifold counting function associated with Laplace--Beltrami eigenvalues. We refine the results of Wyman and Xi, improving their asymptotic: we remove a constant in the codimension-one case, and we prove a new asymptotic in the case that the set of looping times has measure zero.
Disclosure
“+ Cb (|λ + k| + 1)n−d−2 ≤ ϵC λn−d−1 + Cb λn−d−2 , which concludes the proof. □ 4. AI Acknowledgments Claude was used to generate some of the introduction, clean up the writing, and check MatLab code. All substantive results are the work of the author alone. 5. Acknowledgments I’d like to thank my advisor Emmett”
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Structural counts
Pages 12 pdf
Theorems 2 pdf fallback
Lemmas 3 pdf fallback
Propositions 6 pdf fallback
Corollaries 0 pdf fallback
Definitions 0 pdf fallback
Displayed equations 59 pdf fallback
Bibliography entries 13 pdf fallback
Appendix pages 0 estimated
Count notes
- arXiv source was unavailable; PDF-text fallbacks were used.
- Appendix pages include the first PDF page with an explicit Appendix heading through the final page.