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Journal articles

On Kronecker's limit formula and the hypergeometric function.

Abstract : The Kronecker limit formula for a positive definite binary quadratic form or the Dedekind zeta-function of an imaginary quadratic field is quite well-known and there exists an enormous amount of literature pertaining to its proof and applications. Here we give a different kind of proof depending on the hypergeometric transform. The idea goes back to Koshilyakov and we adopted it in this note to give a new derivation of the formula. Here the connection formula for the hypergeometric function plays an essential role.
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Submitted on : Monday, February 2, 2015 - 4:25:47 PM
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S Kanemitsu, Y Tanigawa, H Tsukada. On Kronecker's limit formula and the hypergeometric function.. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2008, Volume 31 - 2008, pp.28-40. ⟨10.46298/hrj.2008.163⟩. ⟨hal-01112329⟩



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