"후르비츠 수 (Hurwitz number)"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) (새 문서: * Bannai, Kenichi, and Shinichi Kobayashi. “Integral Structures on $p$-Adic Fourier Theory.” arXiv:0804.4338 [math], April 28, 2008. http://arxiv.org/abs/0804.4338. * Katz, Nichol...) |
Pythagoras0 (토론 | 기여) |
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| + | ==개요== | ||
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| + | |||
| + | |||
| + | ==$K=Q(\sqrt{-1})$의 예== | ||
| + | * 다음이 성립한다 | ||
| + | $$ | ||
| + | \sum_{ (m,n)\in \mathbb{Z}^2\backslash\{(0,0)\}} \frac{1}{(mi+n)^{4s}}=G_{4s}\omega^{4s},\,s=1,2,\cdots | ||
| + | $$ | ||
| + | 여기서 $G_{s}$는 다음과 같은 상수 | ||
| + | $$ | ||
| + | \begin{array}{c|cccccccc} | ||
| + | s & 4 & 8 & 12 & 16 & 20 & 24 & 28 & 32 \\ | ||
| + | \hline | ||
| + | G_s & \frac{1}{15} & \frac{1}{525} & \frac{2}{53625} & \frac{1}{1243125} & \frac{2}{118096875} & \frac{2}{5575415625} & \frac{4}{527240390625} & \frac{223}{1389278429296875} \\ | ||
| + | \end{array} | ||
| + | $$ | ||
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| + | |||
| + | |||
| + | ==관련논문== | ||
* Bannai, Kenichi, and Shinichi Kobayashi. “Integral Structures on $p$-Adic Fourier Theory.” arXiv:0804.4338 [math], April 28, 2008. http://arxiv.org/abs/0804.4338. | * Bannai, Kenichi, and Shinichi Kobayashi. “Integral Structures on $p$-Adic Fourier Theory.” arXiv:0804.4338 [math], April 28, 2008. http://arxiv.org/abs/0804.4338. | ||
* Katz, Nicholas M. “The Congruences of Clausen — von Staudt and Kummer for Bernoulli-Hurwitz Numbers.” Mathematische Annalen 216, no. 1 (July 1, 1975): 1–4. doi:10.1007/BF02547966. | * Katz, Nicholas M. “The Congruences of Clausen — von Staudt and Kummer for Bernoulli-Hurwitz Numbers.” Mathematische Annalen 216, no. 1 (July 1, 1975): 1–4. doi:10.1007/BF02547966. | ||
2015년 4월 8일 (수) 05:40 판
개요
$K=Q(\sqrt{-1})$의 예
- 다음이 성립한다
$$ \sum_{ (m,n)\in \mathbb{Z}^2\backslash\{(0,0)\}} \frac{1}{(mi+n)^{4s}}=G_{4s}\omega^{4s},\,s=1,2,\cdots $$ 여기서 $G_{s}$는 다음과 같은 상수 $$ \begin{array}{c|cccccccc} s & 4 & 8 & 12 & 16 & 20 & 24 & 28 & 32 \\ \hline G_s & \frac{1}{15} & \frac{1}{525} & \frac{2}{53625} & \frac{1}{1243125} & \frac{2}{118096875} & \frac{2}{5575415625} & \frac{4}{527240390625} & \frac{223}{1389278429296875} \\ \end{array} $$
관련논문
- Bannai, Kenichi, and Shinichi Kobayashi. “Integral Structures on $p$-Adic Fourier Theory.” arXiv:0804.4338 [math], April 28, 2008. http://arxiv.org/abs/0804.4338.
- Katz, Nicholas M. “The Congruences of Clausen — von Staudt and Kummer for Bernoulli-Hurwitz Numbers.” Mathematische Annalen 216, no. 1 (July 1, 1975): 1–4. doi:10.1007/BF02547966.