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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.
https://hal.archives-ouvertes.fr/hal-01112329
Contributor : Ariane Rolland Connect in order to contact the contributor
Submitted on : Monday, February 2, 2015 - 4:25:47 PM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM
Long-term archiving on: : Wednesday, May 27, 2015 - 3:44:16 PM
Contributor : Ariane Rolland Connect in order to contact the contributor
Submitted on : Monday, February 2, 2015 - 4:25:47 PM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM
Long-term archiving on: : Wednesday, May 27, 2015 - 3:44:16 PM
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