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| Kloosterman Sums and a Problem of D. H. Lehmer |
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Citation： |
Ping XI,Yuan YI.Kloosterman Sums and a Problem of D. H. Lehmer[J].Chinese Annals of Mathematics B,2020,41(3):361~370 |
| Page view： 640
Net amount： 1229 |
Authors： |
Ping XI; Yuan YI |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (No.11601413), the Fundamental Research Funds
for the Central Universities (No.201806078) and the Natural
Science Basic Research Plan in Shaanxi Province of China
(No.2017JQ1016). |
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| Abstract： |
A classical problem of D. H. Lehmer suggests the study of
distributions of elements of $\bZ/p\bZ$ of opposite parity to the
multiplicative inverse mod $p$. Zhang initiated this problem and
found an asymptotic evaluation of the number of such elements. In
this paper, an asymptotic formula for the fourth moment of the error
term of Zhang is proved, from which one may see that Zhang's error
term is optimal up to the logarithm factor. The method also applies
to the case of arbitrary positive integral moments. |
Keywords： |
D. H. Lehmer problem, Kloosterman sum, Moment |
Classification： |
11N69, 11L05 |
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