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Sum-Product Estimates Applied to Waring's Problem over Finite Fields
-
Todd Cochrane
and
James Cipra
Published/Copyright:
May 31, 2012
Abstract.
Let A be the set of nonzero k-th powers in 
and 
denote
the minimal n such that 
. We use sum-product estimates for 
and
, following the method of Glibichuk and Konyagin to estimate .
In particular, we obtain that 
for 
provided that exists.
Received: 2011-05-13
Accepted: 2011-10-31
Published Online: 2012-05-31
Published in Print: 2012-June
© 2012 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- On a Theorem of Prachar Involving Prime Powers
- A Novel Approach to the Discovery of Binary BBP-Type Formulas for Polylogarithm Constants
- A Recurrence Related to the Bell Numbers
- Sum-Product Estimates Applied to Waring's Problem over Finite Fields
- Communal Partitions of Integers
- On Computation of Exact van der Waerden Numbers
- On the Complexity of Chooser–Picker Positional Games
- Partition of an Integer into Distinct Bounded Parts, Identities and Bounds
- A Correlation Identity for Stern's Sequence
- Primitive Prime Divisors in Zero Orbits of Polynomials
