论文标题
筛分间隔和西格尔零
Sieving intervals and Siegel zeros
论文作者
论文摘要
假设存在（无限的）siegel零，我们表明，线性筛子中的（rosser-）jurkat-richert界限无法得到改善，同样，同样，请看iWaniec在Jacobsthal的问题上的下限，以及对Brun-Titchmarsh Theorem的较小改进。在这种情况下，我们还推断出在数量之间最长的差距和返工Cramér的启发式方面的最长差距上的改进（尽管有条件）的下限，以表明我们预计差距差距约为$ x $，其差距大约大于$（\ log x）^2 $。
Assuming that there exist (infinitely many) Siegel zeros, we show that the (Rosser-)Jurkat-Richert bounds in the linear sieve cannot be improved, and similarly look at Iwaniec's lower bound on Jacobsthal's problem, as well as minor improvements to the Brun-Titchmarsh Theorem. We also deduce an improved (though conditional) lower bound on the longest gaps between primes, and rework Cramér's heuristic in this situation to show that we would expect gaps around $x$ that are significantly larger than $(\log x)^2$.
