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Kuznecov remainders and generic metrics (2507.06887v1)
Published 9 Jul 2025 in math.AP, math.DG, and math.SP
Abstract: We obtain improved remainder estimates in the Kuznecov sum formula for period integrals of Laplace eigenfunctions on a Riemannian manifold $M$. Building upon the two-term asymptotic expansion established in [arXiv:2204.13525], we prove that for a Baire-generic class of metrics, the oscillatory second term in the Kuznecov formula can be eliminated, yielding an improved remainder estimate.
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