Zeta functions of<Emphasis Type="Italic">q</Emphasis>-perfect numbers |
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| Authors: | Nobushige Kurokawa Wakayama Masato |
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| Institution: | (1) Department of Mathematics, Tokyo Institute of Technology, Oh-okayama Meguro-ku, 152-0033 Tokyo, Japan;(2) Faculty of Mathematics, Kyushu University, Hakozaki Higashi-ku, 812-8581 Fukuoka, Japan |
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| Abstract: | We introduce a notion ofq-analogue of the perfect numbers. We also define a new zeta function which we call a zeta function ofq-perfect numbers. In this paper, the properties of theq-perfect numbers and the zeta functions are studied. Especially, we determine theq-perfect numbers whenq is a root of unity. |
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| Keywords: | 2000 Mathematics Subject Classification" target="_blank">2000 Mathematics Subject Classification 11M36 |
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