K. Lapkova

activity

20152020

most citedDensity of power-free values of polynomials

6 citations · 7 across the 9 of their papers we have counts for

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Showing 2015Show all

3 papers · 1 filter

math.NT2015

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

Kostadinka Lapkova

Consider the divisor sum $\sum_{n \leq N} τ (n^{2} + 2 bn + c)$ for integers $b$ and $c$ which satisfy certain extra conditions. For this average sum we obtain an explicit upper bound, which…

math.NT2015

The class number one problem for the real quadratic fields $Q ((an)^{2} + 4 a)$

András Biró, Kostadinka Lapkova

We solve unconditionally the class number one problem for the $2$ -parameter family of real quadratic fields $Q (d)$ with square-free discriminant $d = (an)^{2} + 4 a$ for p…

math.NT2015

On the $k$ -free values of the polynomial $x y^{k} + C$

Kostadinka Lapkova

Consider the polynomial $f (x, y) = x y^{k} + C$ for $k \geq 2$ and any nonzero integer constant $C$ . We derive an asymptotic formula for the $k$ -free values of $f (x, y)$ when $x, y \leq H$ . W…

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

The class number one problem for the real quadratic fields Q((an)2+4a​)

On the k-free values of the polynomial xyk+C

The class number one problem for the real quadratic fields $Q ((an)^{2} + 4 a)$

On the $k$ -free values of the polynomial $x y^{k} + C$