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January, 2008 On Gauss’ formula for ψ and finite expressions for the L -series at 1
Masahiro HASHIMOTO, Shigeru KANEMITSU, Masayuki TODA
J. Math. Soc. Japan 60(1): 219-236 (January, 2008). DOI: 10.2969/jmsj/06010219


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.


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Masahiro HASHIMOTO. Shigeru KANEMITSU. Masayuki TODA. "On Gauss’ formula for ψ and finite expressions for the L -series at 1." J. Math. Soc. Japan 60 (1) 219 - 236, January, 2008.


Published: January, 2008
First available in Project Euclid: 24 March 2008

zbMATH: 1211.11097
MathSciNet: MR2392009
Digital Object Identifier: 10.2969/jmsj/06010219

Primary: 11R29 , 33B15
Secondary: 11R11

Keywords: Dirichlet class number formula , Gauss formula for the digamma function , Hurwitz zeta-function , Lehmer’s arithmetic function , orthogonality of characters

Rights: Copyright © 2008 Mathematical Society of Japan


Vol.60 • No. 1 • January, 2008
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