|
Universal binary Hermitian forms
Author(s):
A.
G.
Earnest;
Azar
Khosravani.
Journal:
Math. Comp.
66
(1997),
1161-1168.
MSC (1991):
Primary 11E39;
Secondary 11E20, 11E41
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We will determine (up to equivalence) all of the integral positive definite Hermitian lattices in imaginary quadratic fields of class number 1 that represent all positive integers.
References:
- [1]
- W. Chan, M. H. Kim and S. Raghavan, Ternary universal integral quadratic forms over real quadratic fields, preprint.
- [2]
- L. E. Dickson, Quaternary quadratic forms representing all integers, Amer. J. Math. 49 (1947), 39-56.
- [3]
- L. J. Gerstein, Classes of definite Hermitian forms, Amer. J. Math. 100 (1978), pp. 81-97. MR 57:5946
- [4]
- N. Jacobson, A note on hermitian forms, Bull. Amer. Math. Soc. 46 (1940), pp. 264-268. MR 1:325d
- [5]
- A. A. Johnson, Integral representations of hermitian forms over local fields, J. Reine Angew. Math. 229 (1968), pp. 57-80. MR 37:1348
- [6]
- I. Kaplansky, Ternary positive quadratic forms that represent all odd positive integers, Acta Arith. 70 (1995), pp. 209-214. MR 96b:11052
- [7]
- C. G. Lekkerkerker, Geometry of Numbers, North-Holland, Amsterdam-London, 1969. MR 42:5915
- [8]
- H. Maass, Über die Darstellung total positiver Zählen des Korpers
als Summe von drei Quadraten, Abh. Math. Sem. Hamburg, 14, (1941), pp. 185-91. MR 3:163a - [9]
- J. P. Prieto-Cox, Representation of positive definite Hermitian forms, Ph.D. Dissertation, Ohio State University (1990).
- [10]
- S. Ramanujan, On the expression of a number in the form
, Proc. Cambridge Phil. Soc. 19 (1917), 11-21. - [11]
- G. Shimura, Arithmetic of unitary groups, Ann. of Math. 79 (1964), pp. 369-409. MR 28:2104
- [12]
- M. F. Willerding, Determination of all classes of positive quaternary quadratic forms which represent all (positive) integers, Bull. Amer. Math. Soc. 54 (1948), pp. 334-337. MR 9:571e
- [13]
- F. Z. Zhu, On the classification of positive definite unimodular hermitian forms, Chinese Sci. Bull. 36 (1991), 1506-1511. MR 93a:11027
Similar Articles:
Retrieve articles in Mathematics of Computation
with MSC
(1991):
11E39,
11E20, 11E41
Retrieve articles in all Journals with MSC
(1991):
11E39,
11E20, 11E41
Additional Information:
A.
G.
Earnest
Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901--4408
Azar
Khosravani
Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901--4408
Address at time of publication:
Department of Mathematics, University of Wisconsin, Oshkosh, Oshkosh, Wisconsin 54901-8631
DOI:
10.1090/S0025-5718-97-00860-0
PII:
S 0025-5718(97)00860-0
Received by editor(s):
May 15, 1996
Additional Notes:
Research supported in part by a grant from the National Security Agency
Copyright of article:
Copyright
1997,
American Mathematical Society
|