Geodesic
Effective estimates from below of the norms of ideals of an imaginary quadratic field
Sbornik. Mathematics, Tome 11 (1970) no. 1, pp. 47-58 
E. A. Anfert'eva; N. G. Chudakov. Effective estimates from below of the norms of ideals of an imaginary quadratic field. Sbornik. Mathematics, Tome 11 (1970) no. 1, pp. 47-58. http://geodesic.mathdoc.fr/item/SM_1970_11_1_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $K=Q(\sqrt{-\Delta})$ be an imaginary quadratic field with discriminant $-\Delta$, and with ideal class number $h(\Delta)$. It is proved that there exists an ideal class in which the norm of all the integral ideals is not less than $(\lg\Delta)^{-c}\sqrt\Delta$, where the constant $c=c(h)$ can be effectively computed for given $h$. Bibliography: 9 titles.

[1] E. A. Anferteva, N. G. Chudakov, “O minimumakh normennoi funktsii v minimalnykh kvadratichnykh polyakh”, DAN SSSR, 183:2 (1968), 255–256 | MR

[2] N. I. Feldman, “Otsenka lineinoi formy ot logarifmov algebraicheskikh chisel”, Matem. sb., 76(118) (1968), 304–319 | MR

[3] G. Khasse, Lektsii po teorii chisel, IL, Moskva, 1953

[4] N. G. Chudakov, Vvedenie v teorii $L$-funktsii, Moskva

[5] H. Heilbronn, “On the class-number in imajinary quadratic fields”, Quart. J. Math. Oxford Ser., 5:18 (1934), 150–160 | DOI | Zbl

[6] B. A. Venkov, Elementarnaya teoriya chisel, ONTI, Moskva–Leningrad, 1937

[7] A. Beiker, “Lineinye formy ot logarifmov algebraicheskikh chisel. II”, Matematika, 12:4 (1968), 131–136

[8] A. O. Gelfond, Transtsendentnye i algebraicheskie chisla, Gostekhizdat, Moskva, 1952

[9] H. Stark, “A complete determination of the complex quadratic fields of class number one”, Michigan Math. J., 14:1 (1967), 1–27 | DOI | MR | Zbl