Lambert $W$-function and Gauss class number one conjecture

Igor V. Nikolaev

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arXiv · 2512.02232

Lambert $W$-function and Gauss class number one conjecture

Igor V. Nikolaev

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Abstract

We study fixed points of a function arising in a representation theory of the Drinfeld modules by the bounded linear operators on a Hilbert space. We prove that such points correspond to number fields of the class number one. As an application, one gets a solution to the Gauss conjecture for the real quadratic fields of class number one.

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Igor V. Nikolaev. 2025-12-01. Lambert $W$-function and Gauss class number one conjecture. https://arxiv.org/abs/2512.02232

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