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arXiv · 1302.2299

On Improving Roth's Theorem in the Primes

Eric Naslund
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Abstract

Let $A\subset\left\{ 1,\dots,N\right\} $ be a set of prime numbers containing no non-trivial arithmetic progressions. Suppose that $A$ has relative density $\alpha=|A|/\pi(N)$, where $\pi(N)$ denotes the number of primes in the set $\left\{ 1,\dots,N\right\} $. By modifying Helfgott and De Roton's work, we improve their bound and show that $$\alpha\ll\frac{\left(\log\log\log N\right)^{6}}{\log\log N}.$$

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Eric Naslund. 2013-02-10. On Improving Roth's Theorem in the Primes. https://doi.org/10.1112/s0025579314000175

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