Kostadinka Lapkova

Explicit upper bound for the average number of divisors of irreducible quadratic polynomials

Consider the divisor sum

Explicit upper bound for an average number of divisors of quadratic polynomials

\sum _{n\le N}\tau (n^2+2bn+c)

On the average number of divisors of reducible quadratic polynomials

∑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

Divisibility of class numbers of imaginary quadratic fields whose discriminant has only three prime factors

D(-1)

On the k-free values of the polynomial \({xy^k + C}\)

D(-1)-quadruples.

The class number one problem for the real quadratic fields

Consider the divisor sum