Thu Hien Nguyen

activity

20192021

most citedOn the conditions for a special entire function relative to the partial theta-function and the Euler function to belong to the Laguerre-Pólya class

3 citations · 3 across the 4 of their papers we have counts for

collaborators

6 papers

math.CV2021

On the entire functions from the Laguerre-Pólya I class with non-monotonic second quotients of Taylor coefficients

Thu Hien Nguyen, Anna Vishnyakova

We study the entire functions $f (z) = \sum_{k = 0}^{\infty} a_{k} z^{k}, a_{k} > 0,$ with non-monotonic second quotients of Taylor coefficients, namely, such that $\frac{a_{2m-1}^2}{a_{2m-2}a_…

math.CV2021

On the number of real zeros of real entire functions with a non-decreasing sequence of the second quotients of Taylor coefficients

Thu Hien Nguyen, Anna Vishnyakova

For an entire function $f (z) = \sum_{k = 0}^{\infty} a_{k} z^{k},$ $a_{k} > 0,$ we define the sequence of the second quotients of Taylor coefficients $Q := \left( \frac{a_k^2}{a_{k-1}a_{k+1}}…

math.CV2020

On the entire functions from the Laguerre-Pólya I class having the increasing second quotients of Taylor coefficients

Thu Hien Nguyen, Anna Vishnyakova

We prove that if $f (x) = \sum_{k = 0}^{\infty} a_{k} x^{k},$ $a_{k} > 0,$ is an entire function such that the sequence $Q := (\frac{a _{k}^{2}}{a _{k - 1} a _{k + 1}})_{k = 1}^{\infty}$ is non-…

math.CV2020

On the closest to zero roots and the second quotients of Taylor coefficients of entire functions from the Laguerre-Pólya I class

Thu Hien Nguyen, Anna Vishnyakova

For an entire function $f (z) = \sum_{k = 0}^{\infty} a_{k} z^{k}, a_{k} > 0,$ we show that if $f$ belongs to the Laguerre-Pólya class, and the quotients $q_k := \frac{a_{k-1}^2}{a_{k-2}a_k}, k…

math.CV2019★ 3 cited

On the conditions for a special entire function relative to the partial theta-function and the Euler function to belong to the Laguerre-Pólya class

Thu Hien Nguyen

In this paper, we discuss the conditions for the function $F_{a} (z) = \sum_{k = 0}^{\infty} \frac{z ^{k}}{( a + 1 ) ( a ^{2} + 1 ) \dots ( a ^{k} + 1 )}, a > 1,$ to belong to the Laguerre-Pólya class, or to ha…

math.CV2019

On the necessary condition for entire function with the increasing second quotients of Taylor coefficients to belong to the Laguerre-Pólya class

Thu Hien Nguyen, Anna Vishnyakova

For an entire function $f (z) = \sum_{k = 0}^{\infty} a_{k} z^{k}, a_{k} > 0,$ we show that $f$ does not belong to the Laguerre-Pólya class if the quotients $\frac{a _{n - 1}^{2}}{a _{n - 2} a _{n}}$ are i…