{"docId":144,"paperId":144,"url":"https:\/\/hrj.episciences.org\/144","doi":"10.46298\/hrj.2001.144","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":35,"name":"Volume 24 - 2001"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01109799","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-01109799v1","dateSubmitted":"2015-03-03 16:13:54","dateAccepted":"2015-06-12 16:05:45","datePublished":"2001-01-01 08:00:00","titles":{"en":"On the values of the Riemann zeta-function at rational arguments"},"authors":["Kanemitsu, S","Tanigawa, Y","Yoshimoto, M"],"abstracts":{"en":"In a companion paper, ``On multi Hurwitz-zeta function values at rational arguments, Acta Arith. {\\bf 107} (2003), 45-67'', we obtained a closed form evaluation of Ramanujan's type of the values of the (multiple) Hurwitz zeta-function at rational arguments (with denominator even and numerator odd), which was in turn a vast generalization of D. Klusch's and M. Katsurada's generalization of Ramanujan's formula. In this paper we shall continue our pursuit, specializing to the Riemann zeta-function, and obtain a closed form evaluation thereof at all rational arguments, with no restriction to the form of the rationals, in the critical strip. This is a complete generalization of the results of the aforementioned two authors. We shall obtain as a byproduct some curious identities among the Riemann zeta-values."},"keywords":[{"en":" functional equation"},{"en":" modular relation"},{"en":" Ramanujan's type formula"},{"en":" special values at rational arguments"},{"en":"Hurwitz zeta-function"},"[MATH] Mathematics [math]"]}