A logarithm type mean value theorem of the Riemann zeta function |
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Authors: | Xia-Qi Ding |
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Institution: | Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, PR China |
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Abstract: | For any integer K?2 and positive integer h, we investigate the mean value of |ζ(σ+it)|2k×logh|ζ(σ+it)| for all real number 0<k<K and all σ>1−1/K. In case K=2, h=1, this has been studied by Wang in F.T. Wang, A mean value theorem of the Riemann zeta function, Quart. J. Math. Oxford Ser. 18 (1947) 1-3]. In this note, we give a new brief proof of Wang's theorem, and, with this method, generalize it to the general case naturally. |
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Keywords: | 11M06 |
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