Evaluations of New Euler Sums of Even Weight with Dirichlet Characters
碩士 === 國立中正大學 === 應用數學研究所 === 95 === The classical~Euler sum is defined by [ S_{p, q} := sum_{k=1}^{infty} frac{1}{k^{q}} sum_{j=1}^{k} frac{1}{j^{p}}. ] In this thesis, we consider the more general sum defined by [ S_{p, q}^{chi} := sum_{k=1}^{infty} frac{chi(k)}{k^{q}} sum_{j=1}^{k} frac{1}{...
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Format: | Others |
Language: | en_US |
Online Access: | http://ndltd.ncl.edu.tw/handle/18543953312745149511 |
Summary: | 碩士 === 國立中正大學 === 應用數學研究所 === 95 === The classical~Euler sum is defined by
[
S_{p, q} := sum_{k=1}^{infty} frac{1}{k^{q}} sum_{j=1}^{k} frac{1}{j^{p}}.
]
In this thesis, we consider the more general sum defined by
[
S_{p, q}^{chi} := sum_{k=1}^{infty} frac{chi(k)}{k^{q}} sum_{j=1}^{k} frac{1}{j^{p}},
]
where $chi$ is~Dirichlet character. We have evaluations in terms of values at positive
integers of~Herwitz zeta functions, when $chi$ is odd and the weight $w = p+q$ is even.
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