PreprintCC0arXiv
On existence of generalised Lehmer numbers modulo primes
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.
Related
- Zero-Run Spectra of the (3,2) Raney numbers Modulo Primes
- Galois groups of Apéry-like series modulo primes
- On the distribution of αp³ modulo one over special primes
- Notes on Algebraic Properties and Non-Standard Analysis of the Ring of Integers Modulo Infinitely Large Primes
- On periods of the Tribonacci sequence modulo primes
BibTeX
@misc{misra2026existence,
title = {{On existence of generalised Lehmer numbers modulo primes}},
author = {Bikram Misra and Bidisha Roy and B. Sury},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24082},
eprint = {2609.24082},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24082},
note = {CC0},
}
RIS
TY - UNPB
TI - On existence of generalised Lehmer numbers modulo primes
AU - Bikram Misra
AU - Bidisha Roy
AU - B. Sury
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24082
UR - https://arxiv.org/abs/2609.24082
AB - 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.
ER -