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arXiv · 2507.08221

The $p$-adic valuation of local resolvents, generalized Gauss sums and anticyclotomic Hecke $L$-values of imaginary quadratic fields at inert primes

Ashay Burungale·Shinichi Kobayashi·Kazuto Ota
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Abstract

We prove an asymptotic formula for the $p$-adic valuation of Hecke $L$-values of an imaginary quadratic field at an inert prime $p$ along the anticyclotomic $\mathbb{Z}_p$-tower. The key is determination of the $p$-adic valuation of generalized Gauss sums defined using Coates-Wiles homomorphism, and of local resolvents in $\mathbb{Z}_p$-extensions. This answers a question of Rubin.

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Ashay Burungale, Shinichi Kobayashi, Kazuto Ota. 2025-07-10. The $p$-adic valuation of local resolvents, generalized Gauss sums and anticyclotomic Hecke $L$-values of imaginary quadratic fields at inert primes. https://arxiv.org/abs/2507.08221

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