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Long arithmetic progressions in critical sets |
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| Authors: | Ernie Croot |
| Institution: | Georgia Institute of Technology, School of Mathematics, 125 Skiles, Atlanta, GA 30332, USA |
| Abstract: | Given a density 0<σ?1, we show for all sufficiently large primes p that if S⊆Z/pZ has the least number of three-term arithmetic progressions among all sets with at least σp elements, then S contains an arithmetic progression of length at least log1/4+o(1)p. |
| Keywords: | Arithmetic progressions Additive number theory Number theory Arithmetic combinatorics Additive combinatorics Three-term arithmetic progressions |
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