Cassou-Noguès, Pierrette Arithmetic applications of the study of the values at negative integers of Dirichlet series associated with a polynomial. (Applications arithmétiques de l’étude des valeurs aux entiers négatifs des séries de Dirichlet associées à un polynôme.) (French) Zbl 0496.12009 Ann. Inst. Fourier 31, No. 4, 1-35 (1981). Reviewer: Charles J. Parry (Blacksburg) Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 7 Documents MSC: 11S40 Zeta functions and \(L\)-functions 11M41 Other Dirichlet series and zeta functions 30B50 Dirichlet series, exponential series and other series in one complex variable Keywords:continuation of Dirichlet series; zeta(-k); evaluation of zeta function Citations:JFM 30.0201.05; JFM 54.0369.03 × Cite Format Result Cite Review PDF Full Text: DOI Numdam Numdam EuDML References: [1] [1] et , Fonctions zêta p-adiques des corps de nombres abéliens réels, Acta Arithm., Warsawa, 20 (1972), 353-384. · Zbl 0217.04303 [2] [2] , The theory of the double gamma function, Philosophical Transactions of the Royal Society (A), 196 (1901), 265-388. · JFM 32.0442.02 [3] [7] , Schichte Funktionen und BMOA, Comm. Math. Helv., 62 (1977), 591-602. · JFM 35.0462.01 [4] [4] , P-adic Gamma functions and Dwork cohomology, Trans. of the A.M.S., vol. 257, n° 2 (1980), 359-369. · Zbl 0475.14017 [5] [5] , Formes linéaires p-adiques et prolongement analytique, Thèse 3e cycle, Université de Bordeaux I, 1971. [6] [2] , Éléments de Mathématique, Topologie Générale Chap. IX, Hermann, Paris, 1974. · Zbl 0402.12012 [7] [7] , Valeurs aux entiers négatifs des fonctions zêta et fonctions zêta p-adiques, Inventiones Math., 51 (1979), 29-59. · Zbl 0408.12015 [8] [8] , Analogues p-adiques des fonctions Γ-multiples, Astérisque, 61 (1979), 43-55. · Zbl 0425.12018 [9] [9] , Valeurs aux entiers négatifs des séries de Dirichlet associées à un polynôme I, (en préparation). · Zbl 0496.12008 [10] [10] , Valeurs aux entiers négatifs des séries de Dirichlet associées à un polynôme II, (en préparation). · Zbl 0496.12008 [11] [11] , A generalization of Epstein zeta functions, Michigan Math. J., 21 (1974), 45-48. · Zbl 0287.10026 [12] [12] , A note on a functional equation, J. Austral. Math. Soc., 15 (1973), 385-388. · Zbl 0267.10052 [13] [13] , p-adic L-functions and Iwasawa theory, Durham symposium in algebraic number field (A. Fröhlich éd.) New York, London, Academic Press (1977). · Zbl 0393.12027 [14] [14] , , Values of abelian L-functions at negative integers over totally real fields, Inventiones Math., 59 (1980), 227-286. · Zbl 0434.12009 [15] [15] , The p-adic Log gamma function and p-adic Euler constants, Transactions A.M.S., 233 (1977), 321-337. · Zbl 0382.12008 [16] [16] and , On the behaviour of p-adic L-functions at s = 0, Inventiones Math., 50 (1978), 91-102. · Zbl 0441.12003 [17] [17] , On the behaviour of p-adic L-functions (preprint). [18] [18] and , Gauss sum and the p-adic Γ-function, Annals Math., 109 (1979), 569-581. · Zbl 0406.12010 [19] [19] , A short course on some current research in p-adic analysis (Talks given at the Hanoi Mathematical Institute in July 1978). · Zbl 0439.12011 [20] [20] und , Eine p-adische Theorie des Zetawerte I, Einführung der p-adischen Dirichletschen L-functionen, J. für die reine und angew. Math., 214-215 (1964), 328-339. · Zbl 0186.09103 [21] [21] , Eine p-adische Theorie der Zetawerte II, J. reine angew. Math., 274-275 (1975), 224-239. · Zbl 0309.12009 [22] [22] , Über einer Satz von Mellin, Math. Ann., 100 (1928), 384-395. · JFM 54.0369.03 [23] [23] , Eine Formel für den Logarithmus transcendenter Funktionen von endlichem Geschlecht, Acta Soc. Scient. Fennicae, 29 (1900), Nr 4. · JFM 34.0469.03 [24] [24] , A p-adic analogue of the Γ-function, J. Fac. Sci. Univ. Tokyo, 22 (1975), 255-266. · Zbl 0308.12003 [25] [25] , On evaluation of zeta functions of totally real algebraic number fields at non positive integers, J. of Fac. of Sc. Univ. of Tokyo, section 1 (1976), 393-417. · Zbl 0349.12007 [26] [26] , On certain ray class invariants of real quadratic fields, J. Math. Soc. Japan, vol. 30, n° 1 (1978), 136-167. · Zbl 0392.12009 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.