On Gauss' formula for ψ and finite expressions for the L-series at 1

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概要

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• In this paper, we shall prove in Theorem 1 that Gauss’ famous closed formula for the values of the digamma function at rational arguments is equivalent to the well-known finite expression for the L(1,χ), which in turn gives rise to the finite expression for the class number of quadratic fields. We shall also prove several equivalent expressions for the arithmetic function N(q) introduced by Lehmer and reveal the relationships among them.

• 社団法人 日本数学会の論文
• 2008-01-01

著者

• Hashimoto Masahiro

  Department of Mathematics, Wakayama Institute of Technology

• Kanemitsu Shigeru

  Graduate School of Advanced Technology, Kinki University

• Toda Masayuki

  Graduate School Of Advanced Technology Kinki University

• Kanemitsu Shigeru

  Graduate School Of Advanced Technology Kinki University

• Hashimoto Masahiro

  Department Of Mathematics Wakayama College Of Technology

• Hashimoto Masahiro

  Department Of Applied Electronic Engineering Osaka Electro-communication University

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