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Applications of the Sum-Product Theorem in Finite Fields

21st Annual IEEE Conference on Computational Complexity (CCC'06), 2006
Summary form only given. About two years ago Bourgain, Katz and Tao (2004) proved the following theorem, essentially stating that in every finite field, a set which does not grow much when we add all pairs of elements, and when we multiply all pairs of elements, must be very close to a subfield. Theorem 1: (Bourgain et al., 2004) For every /spl epsi/ >
openaire   +1 more source

Sums of Powers of Integers

Series and Products in the Development of Mathematics
Summary We provide a simple recursive method for generating the finite sum of whole number powers of integers. Given that we know only the formula for the sum with power p – 1, this method generates the formula for the sum with power p by a simple ...
R. B. Dozier
semanticscholar   +1 more source

Sums of products of hypergeometric Bernoulli numbers

Journal of Number Theory, 2010
Ken Kamano
exaly  

Sums of products of Apostol–Bernoulli numbers

Ramanujan Journal, 2012
Min-Soo Kim, Su Hu
exaly  

A study in sums of products

Philosophical Transactions Series A, Mathematical, Physical, and Engineering Sciences, 2015
Philippe Michel
exaly  

A note on sums of products of Bernoulli numbers

Applied Mathematics Letters, 2011
Min-Soo Kim
exaly  

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