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On \(L\)-functions associated with the vector space of binary quadratic forms. (English) Zbl 0774.11052

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

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)
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[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)
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