{"docId":178,"paperId":178,"url":"https:\/\/hrj.episciences.org\/178","doi":"10.46298\/hrj.2013.178","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":46,"name":"Volume 36 - 2013"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01112681","repositoryVersion":1,"repositoryLink":"https:\/\/hal.science\/hal-01112681v1","dateSubmitted":"2015-03-03 16:14:06","dateAccepted":"2015-06-12 16:06:05","datePublished":"2013-01-01 08:00:00","titles":{"en":"On the class number formula of certain real quadratic fields"},"authors":["Chakraborty, K","Kanemitsu, S","Kuzumaki, T"],"abstracts":{"en":"In this note we give an alternate expression of class number formula for real quadratic fields with discriminant $d \\equiv 5\\, {\\rm mod}\\, 8$. %Dirichlet's classical class number formula for real quadratic fields expresses `class number' in somewhat `transcend' manner, which was simplified by P. Chowla in the special case when the discriminant $d = p \\equiv 5\\,{\\rm mod}\\, 8$ is a prime. We use another form of class number formula and transform it using Dirichlet's $1\/4$-th character sums. Our result elucidates other generalizations of the class number formula by Mitsuhiro, Nakahara and Uhera for general real quadratic fields."},"keywords":[["Real quadratic field"],["class number formula"],"[MATH] Mathematics [math]"]}