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

collaborators

9 papers

math.NT2020★ 1 cited

Density of power-free values of polynomials II

Kostadinka Lapkova, Stanley Yao Xiao

In this paper we prove that polynomials $F (x_{1}, \dots, x_{n}) \in Z [x_{1}, \dots, x_{n}]$ of degree $d \geq 3$ , satisfying certain hypotheses, take on the expected density of…

math.NT2020

A stratification result for an exponential sum modulo $p^{2}$

Kostadinka Lapkova, Stanley Yao Xiao

In this note we consider algebraic exponential sums over the values of homogeneous nonsingular polynomials $F (x_{1}, \dots, x_{n}) \in Z [x_{1}, \dots, x_{n}]$ in the quotient ri…

math.NT2019

On the average sum of the $k$ -th divisor function over values of quadratic polynomials

Kostadinka Lapkova, Nian Hong Zhou

Let $F (x) \in Z [x_{1}, x_{2}, \dots, x_{n}]$ be a quadratic polynomial in $n \geq 3$ variables with a nonsingular quadratic part. Using the circle method we derive an asymptotic…

math.NT2018★ 6 cited

Density of power-free values of polynomials

Kostadinka Lapkova, Stanley Yao Xiao

We establish asymptotic formulae for the number of $k$ -free values of polynmilas $F (x_{1}, \dots, x_{n}) \in Z [x_{1}, \dots, x_{n}]$ of degree $d \geq 2$ for any $n \geq 1$ , including w…

math.NT2017

On the average number of divisors of reducible quadratic polynomials

Kostadinka Lapkova

We give an asymptotic formula for the divisor sum $\sum_{c < n \leq N} τ ((n - b) (n - c))$ for integers $b < c$ of the same parity. Interestingly, the coefficient of the main term…

math.NT2017

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

Kostadinka Lapkova

Consider the divisor sum $\sum_{n \leq N} τ (n^{2} + 2 bn + c)$ for integers $b$ and $c$ . We extract an asymptotic formula for the average divisor sum in a convenient form, and provide an ex…

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…

Density of power-free values of polynomials II

A stratification result for an exponential sum modulo p2

On the average sum of the k-th divisor function over values of quadratic polynomials

Density of power-free values of polynomials

On the average number of divisors of reducible quadratic polynomials

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

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

A stratification result for an exponential sum modulo $p^{2}$

On the average sum of the $k$ -th divisor function over values of quadratic polynomials

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

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