2870 



Algebraic numbers; Ideals; Resolvable Forms 



2870 



2870 Forms of higher degree which 

 can be considered as products 

 of linear factors; algebraic 

 numbers; ideals. (See also 

 0820.) 



Abelian number- fields (Zahlkorper) . Weber, H. 



Acta Mth. 8 (1886) 193- ; 9 (1887) 105-. 

 , Kronecker's theorem. Hilbert, D. 



Gott. Nr. (1896) 29-. 

 Algebraic composite fields. Hensel, K. Crelle 



J. Mth. 120 (1899) 99-. 



congruences and universal arithmetic. 

 Kronecker, L. Crelle J. Mth. 100 (1887) 

 490-. 



fields, groups of numbers in. Weber, H. 

 Mth. A. 48 (1897) 433-; 49 (1897) 83-; 

 50 (1898) 1-. 



number-field, unimodular substitutions in. 

 Hurwitz, A. Gott. Nr. (1895) 332-. 



fields, historical and bibliographical 

 account. Hilbert, D. D. Mth. Vr. Jbr. 4 

 (1897) 175-. 



, units in. Minkowski, H. Gott. Nr. 

 (1900) 90-. 



numbers. Dedekind, R. Bll. Sc. Mth. As. 

 11 (1876) 278-; 1 (1877) 17-, 69-, 144-, 

 207-. 



. Hurwitz, A. Gott. Nr. (1895) 324-. 



, analogue of Biemann-Boch theorem in 



theory of. Landsberg, G. Mth. A. 50 (1898) 



577-. 

 , arithmetical theory. Hurwitz, A. Gott. 



Nr. (1895) 230-. 

 , class of lowest order containing given 



classes. Kneser, A. Mth. A. 30 (1887) 179-. 

 , criterion. Minkowski, H. Gott. Nr. 



(1899) 64-. 



depending on cube root of given 

 number. Markoff, A. St Pet. Ac. Sc. Mm. 

 38 (1892) No. 9, 37 pp. 



derived from irreducible cubic equation. 



Mathews, G. B. L. Mth. S. P. 24 (1894) 

 327-. 



and function theory. Granwall, H. 

 Stockh. Ofv. (1897) 199-. 



, fundamental equation of a class-domain 



(Gattungsbereich). Mertens, F. Wien Ak. 



Sb. 103 (1894) (Ab. 2a) 5-. 

 of given class-domain. Hensel, K. Crelle 



J. Mth. 101 (1887) 99-. 

 , greatest common divisor. Sochocki, J. 



Prace Mt.-Fiz. 4 (1893) 95-; Fschr. Mth. 



(1893-94) 297-. 

 , logarithms. Stormer, C. C. B. 130 



(1900) 1603-. 



, real, property of whole system. Cantor, 



G. [non M.} [1873] (vn) Crelle J. Mth. 77 

 (1874) 258-. 



Analytical loci. Cauchy,A.L. C. B. 24 (1847) 

 885-. 



Arithmetical demonstration of algebraic theo- 

 rems. Kneser, A. Crelle J. Mth. 102 (1888) 



Aurifeuillians. Cunningham, (Lt.-Col.) A. L. 

 Mth. S. P. 29 (1898) 381-. 



Binary cubic forms, calculation and classifica- 

 tion for negative determinants. Arndt, F. 

 [1851] Grunert Arch. 31 (1858) 335-. 



forms, which cannot represent powers of 

 primes. Gegenbauer, L. Wien Ak. Sb. 97 



(1889) (Ab. 2a) 368-. 



Biquadratic forms, class, prime divisors. Le- 



jeune-Dirichlet, G. Crelle J. 3 (1828) 35-. 

 Class-number divisible by prime X. Kummer, 



E. E. Berl. Ak. Mb. (1874) 239-. 

 for numbers formed from llth and 13th 



roots of unity. Wolfskehl, P. Crelle J. Mth. 



99 (1886) 173-. 

 Classes of resolvable forms. Schering, E. [1868] 



Gott. Ab. 14 (1869) 16 pp. 

 numbers and Hilbert's theorem. Capelli, 



A. Nap. Bd. 35 (1896) 198-. 

 Complex factorisation of numbers. Cauchy, 



A. L. C. B. 24 (1847) 1022- ; 25 (1847) 



46-. 



factors of prime numbers. Zignago, I. Bv. 

 Mt. 4 (1894) 151-. 



number systems, irreducible. Formenti, C. 

 Mil. I. Lomb. Bd. 17 (1884) 6-. 



numbers. Schwering, K. Crelle J. Mth. 

 102 (1888) 56-. 



, advantages of geometric representation. 



Vivanti, G. Bv. Mt. 2 (1892) 167-. 

 , class. Markoff, A. C. B. 112 (1891) 



780-, 1049-, 1123-, 1288. 



connected with equation 6 3 - 2 = 0. 

 Mathews, G. B. L. Mth. S. P. 24 (1893) 

 319-. 



, extension. Vahlen, T. Konigsb. Schr. 



38 (1897) [72]-. 



of form a + bi. Gegenbauer, L. Wien 

 Ak. Sb. 91 (1885) (Ab. 2) 1047-. 



formed from fourth roots of unity. 

 Gegenbauer, L. Wien Ak. D. 50 (1885) 

 (Ab. 1) 153-. 



, probabilities in con- 

 nexion with. Gegenbauer, L. Wien Ak. Sb. 

 98 (1890) (Ab. 2a) 635-. 



, quadratic reciprocity 



law for. Busche, E. Hamb. Mth. Gs. Mt. 

 2 (1890) (Festschr., Tl. 2) 80-. 



, ideal prime factors. Kummer, E. E. 

 Berl. Ab. (1856) (Mth.) 1-. 



, norms. Schwering, K. Acta Mth. 11 



(1887-88) 265-. 

 , systems of, and bilinear groups. Cartan, 



E. Toul. Fac. Sc. A. 12 (1898) B, 99 pp. 

 , , transformation groups. Study, 



E. Mh. Mth. Ps. 1 (1890) 283-. 

 , theory. Ivanov, I. St Pet. Ac. Sc. Mm. 



(Es.) 72 (1893) (Suppl.) No. 9, 14 pp.; Fschr. 



Mth. (1893-94) 302. 



primes. Gegenbauer, L. Wien Ak. Sb. 98 



(1890) (Ab. 2a) 1036-. 



formed from fifth roots of unity. Tanner, 



H. W. L. L. Mth. S. P. 24 (1893) 223-. 

 Cubic number-fields, number of ideal classes 



in. Dedekind, R. Crelle J. Mth. 121 (1900) 



40-. 

 , table of class numbers. Reid, L. W. 



N. Y. Am. Mth. S. Bll. 6 (1900) 268, 277-. 



220 



