Universal binary Hermitian forms
HTML articles powered by AMS MathViewer
- by A. G. Earnest and Azar Khosravani PDF
- Math. Comp. 66 (1997), 1161-1168 Request permission
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
- W. Chan, M. H. Kim and S. Raghavan, Ternary universal integral quadratic forms over real quadratic fields, preprint.
- L. E. Dickson, Quaternary quadratic forms representing all integers, Amer. J. Math. 49 (1947), 39–56.
- Larry J. Gerstein, Classes of definite Hermitian forms, Amer. J. Math. 100 (1978), no. 1, 81–97. MR 466063, DOI 10.2307/2373877
- T. Venkatarayudu, The $7$-$15$ problem, Proc. Indian Acad. Sci., Sect. A. 9 (1939), 531. MR 0000001, DOI 10.1090/gsm/058
- Arnold A. Johnson, Integral representations of hermitian forms over local fields, J. Reine Angew. Math. 229 (1968), 57–80. MR 225755, DOI 10.1515/crll.1968.229.57
- Irving Kaplansky, Ternary positive quadratic forms that represent all odd positive integers, Acta Arith. 70 (1995), no. 3, 209–214. MR 1322563, DOI 10.4064/aa-70-3-209-214
- C. G. Lekkerkerker, Geometry of numbers, Bibliotheca Mathematica, Vol. VIII, Wolters-Noordhoff Publishing, Groningen; North-Holland Publishing Co., Amsterdam-London, 1969. MR 0271032
- Sergio Sispanov, Generalización del teorema de Laguerre, Bol. Mat. 12 (1939), 113–117 (Spanish). MR 3
- J. P. Prieto-Cox, Representation of positive definite Hermitian forms, Ph.D. Dissertation, Ohio State University (1990).
- S. Ramanujan, On the expression of a number in the form $ax^{2} + by^{2} +cz^{2} +du^{2}$, Proc. Cambridge Phil. Soc. 19 (1917), 11–21.
- Goro Shimura, Arithmetic of unitary groups, Ann. of Math. (2) 79 (1964), 369–409. MR 158882, DOI 10.2307/1970551
- Garrett Birkhoff and Morgan Ward, A characterization of Boolean algebras, Ann. of Math. (2) 40 (1939), 609–610. MR 9, DOI 10.2307/1968945
- Fu Zu Zhu, On the classification of positive definite unimodular Hermitian forms, Chinese Sci. Bull. 36 (1991), no. 18, 1506–1511. MR 1147259
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
- Received by editor(s): May 15, 1996
- Additional Notes: Research supported in part by a grant from the National Security Agency
- © Copyright 1997 American Mathematical Society
- Journal: Math. Comp. 66 (1997), 1161-1168
- MSC (1991): Primary 11E39; Secondary 11E20, 11E41
- DOI: https://doi.org/10.1090/S0025-5718-97-00860-0
- MathSciNet review: 1422787