On Kronecker's limit formula and the hypergeometric function.

S Kanemitsu (1) , Y Tanigawa (2) , H Tsukada (1)

1 University ok Kinki
2 Graduate School of Mathematics [Nagoya]

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.

Mots clés: Kronecker limit formula; positive definite binary quadratic form; Dedekind zeta-function; hypergeometric function; hypergeometric transform; connection formula

Domaines: Mathématiques [math]

S Kanemitsu, Y Tanigawa, H Tsukada. On Kronecker's limit formula and the hypergeometric function.. Hardy-Ramanujan Journal, 2008, Volume 31 - 2008, pp.28-40. ⟨10.46298/hrj.2008.163⟩. ⟨hal-01112329⟩