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arXiv · 2507.06887

Kuznecov remainders and generic metrics

Vadim Kaloshin·Emmett L. Wyman·Yakun Xi
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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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Vadim Kaloshin, Emmett L. Wyman, Yakun Xi. 2025-07-09. Kuznecov remainders and generic metrics. https://arxiv.org/abs/2507.06887

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