当前位置: X-MOL 学术Monatshefte Math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Explicit upper bound for the average number of divisors of irreducible quadratic polynomials
Monatshefte für Mathematik ( IF 0.8 ) Pub Date : 2017-05-27 , DOI: 10.1007/s00605-017-1061-y
Kostadinka Lapkova 1
Affiliation  

Consider the divisor sum $$\sum _{n\le N}\tau (n^2+2bn+c)$$∑n≤Nτ(n2+2bn+c) for integers b and c. We extract an asymptotic formula for the average divisor sum in a convenient form, and provide an explicit upper bound for this sum with the correct main term. As an application we give an improvement of the maximal possible number of $$D(-1)$$D(-1)-quadruples.

中文翻译:

不可约二次多项式的平均除数的显式上限

考虑整数 b 和 c 的除数和 $$\sum _{n\le N}\tau (n^2+2bn+c)$$∑n≤Nτ(n2+2bn+c)。我们以一种方便的形式为平均除数和提取了一个渐近公式,并为这个和提供了一个明确的上界,并带有正确的主项。作为一个应用程序,我们对 $$D(-1)$$D(-1)-四元组的最大可能数量进行了改进。
更新日期:2017-05-27
down
wechat
bug