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On Rapid Generation of SL2(๐ฝq)
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Jeremy Chapman
Published/Copyright:
May 7, 2009
Abstract
We prove that if A โ ๐ฝq\{0} with 
, then |R(A) ยท R(A)| โฅ Cโฒq3, where
The proof relies on a result, previously established by D. Hart and the author (Iosevich, Contemporary Math.), which implies that if |A| is much larger than 
then
|{(a11, a12, a21, a22) โ A ร A ร A ร A : a11a22 โ a12a21 = 1}| = |A|4qโ1(1 + o(1)).
Received: 2008-09-30
Accepted: 2008-11-19
Published Online: 2009-05-07
Published in Print: 2009-April
ยฉ de Gruyter 2009
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- On k-Imperfect Numbers
- On Universal Binary Hermitian Forms
- The Shortest Game of Chinese Checkers and Related Problems
- On Two-Point Configurations in a Random Set
- On Rapid Generation of SL2(๐ฝq)
- Tiling Proofs of Some Formulas for the Pell Numbers of Odd Index
- Some new van der Waerden numbers and some van der Waerden-type numbers
- Integer Partitions into Arithmetic Progressions with an Odd Common Difference
- On Asymptotic Constants Related to Products of Bernoulli Numbers and Factorials
Articles in the same Issue
- On k-Imperfect Numbers
- On Universal Binary Hermitian Forms
- The Shortest Game of Chinese Checkers and Related Problems
- On Two-Point Configurations in a Random Set
- On Rapid Generation of SL2(๐ฝq)
- Tiling Proofs of Some Formulas for the Pell Numbers of Odd Index
- Some new van der Waerden numbers and some van der Waerden-type numbers
- Integer Partitions into Arithmetic Progressions with an Odd Common Difference
- On Asymptotic Constants Related to Products of Bernoulli Numbers and Factorials
