scholarly journals A new transference theorem in the geometry of numbers and new bounds for Ajtai's connection factor

2003 ◽  
Vol 126 (1) ◽  
pp. 9-31 ◽  
Author(s):  
Jin-Yi Cai
Keyword(s):  
Geometry Of Numbers ◽  
Transference Theorem

THE GEOMETRY OF NUMBERS

Nature ◽  
1947 ◽  
Vol 159 (4029) ◽  
pp. 104-105 ◽  
Keyword(s):  
Geometry Of Numbers

scholarly journals Counting Bounded Elements of a Number Field

2020 ◽  
Author(s):  
Mikołaj Fraczyk ◽  
Gergely Harcos ◽  
Péter Maga
Keyword(s):  
Group Theory ◽  
Number Field ◽  
Geometry Of Numbers ◽  
Combine Group ◽  
Successive Minima ◽  
Ideal Lattices ◽  
Linearly Independent ◽  
Ramification Theory

Abstract We estimate, in a number field, the number of elements and the maximal number of linearly independent elements, with prescribed bounds on their valuations. As a by-product, we obtain new bounds for the successive minima of ideal lattices. Our arguments combine group theory, ramification theory, and the geometry of numbers.

scholarly journals Geometry of Numbers Proof of Götzky's Four-Squares Theorem

2002 ◽  
Vol 96 (2) ◽  
pp. 417-431
Author(s):  
Jesse Ira Deutsch
Keyword(s):  
Geometry Of Numbers
Sign in / Sign up

Export Citation Format

Share Document