论文标题
在代数数字段中短时间间隔奇异系列和素数的总和
Sums of singular series and primes in short intervals in algebraic number fields
论文作者
论文摘要
格罗斯（Gross）和史密斯（Smith）提出了Hardy -Littlewood Twin Prime的概括，该猜想是代数数字的。我们估计在这些猜想中产生的单数系列总和的行为，最多是较低的项。更确切地说，我们发现渐近公式用于单数系列的平滑总和减去一个。基于严重和史密斯的猜想，我们使用结果表明，对于代数数字k中的足够大的“短间隔”，在随机短时间间隔中，素数元素计数的差异与cramer模型的偏离偏离了cramer模型的预测，独立于K。猜想在数量上的猜想范围内构成了goldston和goldston和montegersy的经典猜想，而不是刻有怪物。提供了支持猜想的数值数据。
Gross and Smith have put forward generalizations of Hardy - Littlewood twin prime conjectures for algebraic number fields. We estimate the behavior of sums of a singular series that arises in these conjectures, up to lower order terms. More exactly, we find asymptotic formulas for smoothed sums of the singular series minus one. Based upon Gross and Smith's conjectures, we use our result to suggest that for large enough 'short intervals' in an algebraic number field K, the variance of counts of prime elements in a random short interval deviates from a Cramer model prediction by a universal factor, independent of K. The conjecture over number fields generalizes a classical conjecture of Goldston and Montgomery over the integers. Numerical data is provided supporting the conjecture.
