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The Empty Sphere

Published online by Cambridge University Press:  20 November 2018

R. M. Erdahl  and
S. S. Ryshkov
R. M. Erdahl
Affiliation:
Queen's University, Kingston, Ontario
S. S. Ryshkov
Affiliation:
Steklov Institute, Moscow, U.S.S.R.
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In 1924 at the Toronto meeting of the International Congress of Mathematicians, B. N. Delone introduced his empty sphere method for lattices. We have titled our paper after this method as a tribute to his memory.

We have studied the sets of integer solutions of equations of the form

1

where f satisfies the following condition in which Z denotes the integers,

2

and have resolved this problem using the theory of L-types of lattices [3, 4, 11]. We have been able to give a complete description of all such integer solutions when n ≦ 4.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 39 , Issue 4 , 01 August 1987 , pp. 794 - 824
Copyright
Copyright © Canadian Mathematical Society 1987

References

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