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arXiv · 2609.24082

On existence of generalised Lehmer numbers modulo primes

Bikram Misra·Bidisha Roy·B. Sury
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Abstract

In this article, we discuss a multivariable analogue of Lehmer's parity problem. We generalise the notions of Lehmer numbers as Lehmer $q$-tuples for a fixed odd prime $q$. We count the number of Lehmer $q$-tuples and derive an asymptotic estimate with explicit error terms. This deals with estimating various character sums and Deligne's bound for incomplete exponential sums.

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Bikram Misra, Bidisha Roy, B. Sury. 2026-09-21. On existence of generalised Lehmer numbers modulo primes. https://arxiv.org/abs/2609.24082

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