Saito, Hiroshi On \(L\)-functions associated with the vector space of binary quadratic forms. (English) Zbl 0774.11052 Nagoya Math. J. 130, 149-176 (1993). The author proves the analytic continuation and the functional equation of the \(L\)-functions associated with the vector space of binary quadratic forms and determines their poles and residues following T. Shintani [J. Fac. Sci., Univ. Tokyo, Sect. I A 22, 25–65 (1975; Zbl 0313.10041)] and F. Sato [ibid. 28, 585–604 (1981; Zbl 0497.10011)]. The analytic properties of the \(L\)-function of the space of symmetric matrices of degree larger than 2 have been studied by F. Sato [Adv. Stud. Pure Math. 15, 465–508 (1989; Zbl 0714.11053)] and the author [J. Reine Angew. Math. 416, 91-142 (1991; Zbl 0717.11053)]. Reviewer: H.Saito Cited in 6 Documents MSC: 11M41 Other Dirichlet series and zeta functions 14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) 11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) Keywords:analytic continuation; functional equation; \(L\)-functions; binary quadratic forms; poles; residues Citations:Zbl 0313.10041; Zbl 0497.10011; Zbl 0714.11053; Zbl 0717.11053 PDFBibTeX XMLCite \textit{H. Saito}, Nagoya Math. J. 130, 149--176 (1993; Zbl 0774.11052) Full Text: DOI References: [1] DOI: 10.2969/jmsj/02410132 · doi:10.2969/jmsj/02410132 [2] Sugaku no Ayumi 15 pp 85– (1970) [3] Advanced Studies in Pure Math. 15 pp 465– (1989) [4] J. Fac. Sci. Univ. Tokyo 22 pp 25– (1975) [5] Advanced Studies in Pure Math 15 pp 465– (1989) [6] Math. 416 pp 91– (1991) [7] Generalized functions 1 (1964) [8] DOI: 10.1007/BF01078276 · Zbl 0208.15201 · doi:10.1007/BF01078276 [9] J. Fac. Sci. Univ. Tokyo 28 pp 585– (1982) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.