Abstract
By using the properties of trigonometric sums and the estimates of $n$-dimensional Kloosterman sums, we study the high-dimensional D. H. Lehmer problem over incomplete intervals. First we generalize the previous results in [11] by presenting some sharp asymptotic formulae. Then with the aid of a more elementary method, we improve the error terms in a straight-forward manner.
Funding Statement
This work is supported by the N.S.F. (11971381, 11701447,
11871317) of China and the Basic Research Program for Nature Science of Shaanxi Province
(2014JM1001, 2015KJXX-27, 2017JQ1002, 2021JC-29).
Acknowledgments
The authors are grateful to the anonymous referee for very helpful and detailed comments. The authors are also indebted to Professor Igor E. Shparlinski for his kind suggestions and nice reference of [8].
Citation
Di Han. Zhefeng Xu. Yuan Yi. Tianping Zhang. "A Note on High-dimensional D. H. Lehmer Problem." Taiwanese J. Math. 25 (6) 1137 - 1157, December, 2021. https://doi.org/10.11650/tjm/210705
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