Journal of the Ramanujan Mathematical Society

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Milnor’s Multiple Gamma Functions


Affiliations
1 Department of Mathematics, Tokyo Institute of Technology, Oh-Okayama Meguro, Tokyo-152-0033, Japan
2 Department of Mathematics, Nagoya University, Chikusa, Nagoya-464-8602, Japan
3 Kyushu University, Hakozaki Fukuoka-812-8581, Japan
     

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We study basic properties of Milnor’s multiple gamma functions. Moreover, we introduce new multiple sine functions from these Milnor’s functions and show the difficult special values of the Dirichlet L-functions can be expressed by these functions.
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  • Milnor’s Multiple Gamma Functions

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Authors

Nobushige Kurokawa
Department of Mathematics, Tokyo Institute of Technology, Oh-Okayama Meguro, Tokyo-152-0033, Japan
Hiroyuki Ochiai
Department of Mathematics, Nagoya University, Chikusa, Nagoya-464-8602, Japan
Masato Wakayama
Kyushu University, Hakozaki Fukuoka-812-8581, Japan

Abstract


We study basic properties of Milnor’s multiple gamma functions. Moreover, we introduce new multiple sine functions from these Milnor’s functions and show the difficult special values of the Dirichlet L-functions can be expressed by these functions.