×

zbMATH — the first resource for mathematics

Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer. (English) Zbl 0506.14039

MSC:
11G40 \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
11G15 Complex multiplication and moduli of abelian varieties
11G05 Elliptic curves over global fields
14H45 Special algebraic curves and curves of low genus
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Arthaud, N.: On Birch and Swinnerton-Dyer’s conjecture for elliptic curves with complex multiplication. I. Comp. Math.37, 209-232 (1978) · Zbl 0396.12011
[2] Arthaud, N.: Thesis, Stanford University (1978)
[3] Bertrand, D.: Problèmes arithmétiques liés à l’exponentiellep-adique sur les courbes elliptiques. C.R. Acad. Sci. Paris Sér. A282, 1399-1401 (1976) · Zbl 0331.14014
[4] Brumer, A.: On the units of algebraic number fields. Mathematika14, 121-124 (1967) · Zbl 0171.01105
[5] Cassels, J.W.S.: Arithmetic on curves of genus 1 (VIII). J. Reine Angew. Math.217, 180-199 (1965) · Zbl 0241.14017
[6] Coates, J., Wiles, A.: On the conjecture of Birch and Swinnerton-Dyer. Invent. Math.39, 223-251 (1977) · Zbl 0359.14009
[7] Coates, J., Wiles, A.: Onp-adicL-functions and elliptic units. J. Austral. Math. Soc.26, 1-25 (1978) · Zbl 0442.12007
[8] Coleman, R.: Division values in local fields. Invent. Math.53, 91-116 (1979) · Zbl 0429.12010
[9] Goldstein, C., Schappacher, N.: Series d’Eisenstein et fonctionsL de courbes elliptiques à multiplication complexe. To appear in J. Reine Angew. Math. · Zbl 0456.12007
[10] Gross, B.: Arithmetic on Elliptic Curves with Complex Multiplication. Lect. Notes Math.776, New York: Springer (1980) · Zbl 0433.14032
[11] Lubin, J., Tate, J.: Formal complex multiplication in local fields. Ann. of Math.81, 380-387 (1965) · Zbl 0128.26501
[12] Robert, G.: Unites Elliptiques. Bull. Soc. Math. France, Suppl., Memoire36 (1973) · Zbl 0311.12006
[13] Serre, J.P., Tate, J.: Good reduction of abelian varieties. Ann. of Math.88, 492-517 (1968) · Zbl 0172.46101
[14] Shimura, G.: Introduction to the Arithmetic Theory of Automorphic Functions. Princeton Univ. Press, Princeton (1971) · Zbl 0221.10029
[15] Shimura, G.: On the zeta-function of an abelian variety with complex multiplication. Ann. of Math.94, 504-533 (1971) · Zbl 0242.14009
[16] Tate, J.: Algorithm for determining the type of a singular fibre in an elliptic pencil. In: Modular Forms of One Variable (IV). Lect. Notes Math.476, New York: Springer (1975) · Zbl 1214.14020
[17] Weil, A.: Adeles and Algebraic Groups. Inst. for Adv. Study, Princeton (1961) · Zbl 0109.02101
[18] Wiles, A.: Higher explicit reciprocity laws. Ann. of Math.107, 235-254 (1978) · Zbl 0378.12006
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.