Timeline for A variant of the Green-Tao theorem
Current License: CC BY-SA 4.0
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| Aug 10, 2023 at 17:37 | comment | added | Terry Tao | This particular sum can be handled by the classical circle method in the bulk region where $x, x-2y, x+2y \asymp X^{1/3}$, and some standard upper bound sieve to handle the tail region where $x-2y = o(X^{1/3})$. For longer progressions, one can use the asymptotics in my later paper with Ben mathscinet.ams.org/mathscinet/article?mr=2680398 . There are now also estimates that can handle narrow arithmetic progressions, e.g., Theorem 1.7 of arxiv.org/abs/2204.03754 . | |
| Aug 10, 2023 at 13:15 | history | asked | Stanley Yao Xiao | CC BY-SA 4.0 |