HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
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.
Document type :
Journal articles
Complete list of metadata

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

File

31Article3.pdf
Explicit agreement for this submission

Identifiers

Collections

Citation

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⟩

Share

Metrics

Record views

108

Files downloads

338