An algorithm for computing genera of ternary and quaternary quadratic forms

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An algorithm for computing genera of ternary and quaternary quadratic forms

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1991 international symposium on Symbolic and algebraic computation table of contents

Bonn, West Germany

Pages: 134 - 143

Year of Publication: 1991

ISBN:0-89791-437-6

Author

Rainer Schulze-Pillot

Fakultät f. Mathematik, SFB 343, Universität Bielefeld, D-4800 Bielefeld

Sponsors

GMD : German Natl Research Ctr for Information Tech. - Gesellschft
German Comp Soc : GI - Gesellshaft for Informatik
SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

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ACM New York, NY, USA

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REFERENCES

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	Ba	E. Bannai" Positive definite unimodular lattices with trivial automorphism group, Memoirs of the AMS 429 (1990)
	Bi	J. Biermann: Gitter mit kleiner Automorphismengruppe in Geschlechtern von Z-Gittern mit positiv definiter quadratischer Form, Dissertation Gbttingen 1981
	BH	J.W. Senham, J.S. Hsia: Spinor equivalence of quadratic forms, J. of Number Wh. 17, 337-342 (1983)
	BS	S. Bbcherer, R. Schulze-Pillot: Siegel modular forms and theta series attached to quaternion algebras, Preprint 1989 (Preprint Nr. A89-16 FU Berlin)
	BI	H. Brandt, O. Intrau: Tabellen reduzierter positiver tern~irer quadratischer Formen, Abh. S~ichs. Akad. Wiss. Math.-Nat. K1. 45 (1958)
	Ca	J.W.S. Cassels: Rational Quadratic Forms, London ... 1978. Academic Press
	CS	J. H. Conway , N. J. A. Sloane , E. Bannai, Sphere-packings, lattices, and groups, Springer-Verlag New York, Inc., New York, NY, 1987
	Di	L.E. Dickson: Theory of Numbers, New York 1930. Chelsea
	EH	A.G. Earnest, J.S. Hsia: Spinor norms of local integral rotations II, Pac. J. Math. 61, 71-86 (1975), correction: Pac. J. Math. 115,493-494 (1984)
	E1	M. Eichler: Die ~hnlichkeitsklassen indefiniter Gitter, Math. Z. 55, 216-252 (1951/52)
	E2	M. Eichler: Quadratische Formen und Orthogonale Gruppen, Gbttingen ... 1952. Springer
	Ge	K. Germann: Tabellen reduzierter, positiver quatern~rer quadratischer Formen, Comm. Math. Helv. 38, 56-83
	He	E. Hecke: Mathematische Werke, Gbttingen 1970. Vandenhoeck u. Ruprecht
	Kn1	M. Kneser: Klassenzahlen definiter quadratischer Formen, Arch. Math. 8, 241-250 (1957)
	Kn2	M. Kneser: Starke Approximation in algebraischen Gruppen I, J. f. d. reine u. angew. Math. 218, 190-203 (1965)
	Kn3	M. Kneser: Klassenzahlen indefiniter quadratischer Formen in drei oder mehr Ver~nderlichen, Arch. Math. 7, 323-332 (1956)
	Kn4	M. Kneser: Quadratische Formen, Vorlesungsausarbeitung Gbttingen 1973/74
	KV	H. Koch, B.B. Venkov" Uber ganzzahlige unimodulare euklidische Gitter, J. f. d. reine u. angew. Math. 398, 144-168 (1989)
	LPS	A. Lubotzky, R. Phillips, P. Sarnak: Ramanujan graphs, Combinatorica 8, 261-277 (1988)
	Mi1	H. Minkowski: Sur la r~duction des formes quadratiques positives quaternaires, Comptes rendus de l'Acad. Sci. Paris 96, 1205-1210 (1883)
	Mi2	H. Minkowski: Diskontinuitttsbereich ftir arithmetische .~quivalenz, J. f. d. reine u. angew. Math. 129, 220-274 (1905)
	Ni	H.-V. Niemeier: Definite quadratische Formen der Dimension 24 und Diskriminante i, 3. of Number Th. 5, 142-178 (1973)
	OM	O.T. O'Meara: Introduction to Quadratic Forms, Berlin ... 1971. Springer
	Pi1	A. Pizer: An algorithm for computing modular forms on r0(N), J. of Algebra 64, 340-390 (1980)
	Pi2	A. Bizet: Ramanujan graphs and Hecke operators, Bull. AMS 23, 127-138 (1990)
	PZ	M. Pohst , H. Zassenhaus, Algorithmic algebraic number theory, Cambridge University Press, New York, NY, 1989
	Poh	Michael Pohst, Computation of integral solutions of a special type of systems of quadratic equations, Proceedings of the European Computer Algebra Conference on Computer Algebra, p.203-213, March 28-30, 1983
	Pon	P. Ponomarev: Class numbers of definite quaternary forms with square discriminant, J. of Number wh. 6, 291-317 (1974)
	Schi	A. Schiemann: Ein Beispiel positiv definiter quadratischer Formen der Dimension 4 mit gleichen Darstellungszahlen, Arch.Math 54, 372-375 (1990)
	SP1	R. Schulze-Pillot" Darstellung dutch definite tern~ire quadratische Formen, J. of Number Th. 14, 237-250 (1982)
	SP2	R. Schulze-Pillot: A linear relation between theta series of degree and weight 2, p. 197-201 in Number Theory, Ulm 1987, Lect. Notes in Math. 1380, New York ... 1989. Springer
	Shi	K.-I. Shiota: On theta series and the splitting of S2(F0(q)), Preprint
	To	S.B. Townes: Table of reduced positive quaternary quadratic forms, Ann. of Math. 41, 57-58 (1940)
	Vi	M.F. Vigneras: Arithmdtiques des Alg~bres de Quaternions, Lect. Notes Math. 800, Berlin ... 1980. Springer
	vdW	B.L.v.d. Waerden: Die Reduktionstheorie der positiven quadratischen Formen, Acta Math. 96, 265-309 (1956)
	Ya	T. Yamazaki" Jacobi forms and a Maass relation for Eisenstein series (2), Preprint 1988 (Math. Gottingensis Heft 31)