论文标题
$ e_2 $ numbers的Sono多维筛子的明确计算
Explicit Calculations for Sono's Multidimensional Sieve of $E_2$-Numbers
论文作者
论文摘要
我们为Keiju Sono在$ e_2 $ -numbers的多维筛子中使用的某些对称多项式的积分提供了明确的公式，即是两个不同素数的产品。我们使用这些计算来生成当前最著名的界限，以解决多个$ e_2 $ numbers之间的差距。例如，我们表明，在无条件的94个差距大小内，有四个$ e_2 $ numbers的出现，差距大小不超过32，假设Elliott-Halberstam猜想了质数和筛选$ e_2 $ -numbers。
We derive explicit formulas for integrals of certain symmetric polynomials used in Keiju Sono's multidimensional sieve of $E_2$-numbers, i.e., integers which are products of two distinct primes. We use these computations to produce the currently best-known bounds for gaps between multiple $E_2$-numbers. For example, we show there are infinitely many occurrences of four $E_2$-numbers within a gap size of 94 unconditionally and within a gap size of 32 assuming the Elliott-Halberstam conjecture for primes and sifted $E_2$-numbers.
