| Hardy和Littlewood的一个三角和 |
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| 引用本文： | 何圆. Hardy和Littlewood的一个三角和[J]. 数学学报, 1936, 63(3): 271-280 |
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| 作者姓名： | 何圆 |
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| 作者单位： | 内江师范学院数学与信息科学学院 内江 641100 |
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| 基金项目： | 国家自然科学基金资助项目（11326050） |
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| 摘 要： | 本文对Hardy和Littlewood考虑的一个有限三角和做了进一步地研究.通过充分运用Chebyshev多项式和Möbius函数的性质，建立了该有限三角和的一个有趣的恒等式，并得到了一个精确的渐近公式.
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On a Trigonometric Sum of Hardy and Littlewood |
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| Yuan HE. On a Trigonometric Sum of Hardy and Littlewood[J]. Acta Mathematica Sinica, 1936, 63(3): 271-280 |
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| Authors: | Yuan HE |
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| Affiliation: | School of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, P. R. China |
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| Abstract: | In this paper, we perform a further investigation for a finite trigonometric sum considered by Hardy and Littlewood. By making use of some properties for the Chebyshev polynomials and M¨ obius function, we establish an interesting identity for the finite trigonometric sum of Hardy and Littlewood, by virtue of which an explicit asymptotic formula is also derived. |
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| Keywords: | finite trigonometric sums Chebyshev polynomials Möbius function combinatorial identities |
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