Gauss composition and generalizations

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2369, Issue , 2002, Pages 1-8

  Bhargava, Manjul ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS;

ALGORITHMIC APPLICATIONS; GAUSS COMPOSITIONS;

NUMBER THEORY;

EID: 84958527948     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45455-1_1     Document Type: Conference Paper

References (16)

1. K. Belabas, A fast algorithm to compute cubic fields, Math. Comp. 66 (1997), no. 219, 1213–1237.
2. M. Bhargava, Higher Composition Laws, Ph. D. Thesis, Princeton University, 2001.
3. M. Bhargava, Higher composition laws I–V, in progress.
4. D. Buell, Binary quadratic forms. Classical theory and modern computations, Springer-Verlag, New York, 1989.
5. H. Cohen, A course in computational algebraic number theory, Graduate Texts in Mathematics 138, Springer-Verlag, Berlin, 1993.
6. H. Cohen, Advanced topics in computational number theory, Graduate Texts in Mathematics 193, Springer-Verlag, New York, 2000.
7. H. Davenport and H. Heilbronn, On the density of discriminants of cubic fields II, Proc. Roy. Soc. London Ser. A 322 (1971), no. 1551, 405–420.
8. B. N. Delone and D. K. Faddeev, The theory of irrationalities of the third degree, AMS Translations of Mathematical Monographs 10, 1964.
9. C. F. Gauss, Disquisitiones Arithmeticae, 1801.
10. C. Hermite, Sur la réduction des formes cubiques à deux indéterminées, C. R. Acad. Sci. Paris 48 (1859), 351–357.
11. G. B. Mathews and W. E. H. Berwick, On the reduction of arithmetical binary cubics which have a negative determinant, Proc. Lond. Math. Soc. (2) 10 (1912), 48–53.
12. M. Sato and T. Kimura, A classification of irreducible prehomogeneous vector spaces and their relative invariants, Nagoya Math. J. 65 (1977), 1–155.
13. A. Seidenberg, A new decision method for elementary algebra, Ann. Math. 60 (1954), 365–374.
14. C. L. Siegel, The average measure of quadratic forms with given determinant and signature, Ann. Math. (2) 45 (1944), 667–685.
15. A. Tarski, A decision method for elementary algebra and geometry, 2nd ed., revised, Berkeley and Los Angeles, 1951.
16. D. J. Wright and A. Yukie, Prehomogeneous vector spaces and field extensions, Invent. Math. 110 (1992), 283–314.