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- W3217148045 abstract "Under the assumption of infinitely many Siegel zeroes $s$ with $Re(s)>1-frac{1}{(log q)^{r^r}}$ for a sufficiently large value of $r$, we prove that there exist infinitely many $m$-tuples of primes that are $ll e^{1.9828m}$ apart. This improves (in some sense) on the bounds of Maynard-Tao, Baker-Irving, and Polymath 8b, who found bounds of $e^{3.815m}$ unconditionally and $me^{2m}$ assuming the Elliott-Halberstam conjecture; it also generalizes a 1983 result of Heath-Brown that states that infinitely many Siegel zeroes would imply infinitely many twin primes. Under this assumption of Siegel zeroes, we also improve the upper bounds for the gaps between prime pairs, triples, quadruples, quintuples, and sextuples beyond the bounds found via Elliott-Halberstam." @default.
- W3217148045 created "2021-12-06" @default.
- W3217148045 creator A5058933245 @default.
- W3217148045 date "2021-11-28" @default.
- W3217148045 modified "2023-09-27" @default.
- W3217148045 title "Prime Tuples and Siegel Zeros" @default.
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