Ioulia N. Baoulina

activity

20162018

collaborators

8 papers

math.NT2018

Integer ratios of consecutive alternating power sums

Ioulia N. Baoulina

We give a characterization of all pairs $(k, n)$ of positive integers for which the ratio $\frac{1 ^{k} - 2 ^{k} + 3 ^{k} - \dots + ( - 1 ) ^{n + 1} n ^{k}}{1 ^{k} - 2 ^{k} + 3 ^{k} - \dots + ( - 1 ) ^{n} ( n - 1 ) ^{k}}$ of two con…

math.NT2018

On the unsolvability of certain equations of Erdős-Moser type

Ioulia N. Baoulina

Let $S_{k} (m) := \sum_{j = 1}^{m - 1} j^{k}$ denote a power sum. In 2011, Kellner proposed the conjecture that for $m > 3$ the ratio $S_{k} (m + 1) / S_{k} (m)$ is never an integer, or, equivalently, tha…

math.NT2017

A generalization of the theorems of Chevalley-Warning and Ax-Katz via polynomial substitutions

Ioulia N. Baoulina, Anurag Bishnoi, Pete L. Clark

We give conditions under which the number of solutions of a system of polynomial equations over a finite field F_q of characteristic p is divisible by p. Our setup involves the sub…

math.NT2017

On a theorem of Morlaye and Joly and its generalization

Ioulia N. Baoulina

We show that a weaker version of the well-known theorem of Morlaye and Joly on diagonal equations is a simple consequence of a restricted variable version of the Chevalley-Warning…

math.NT2017

On period polynomials of degree $2^{m}$ and weight distributions of certain irreducible cyclic codes

Ioulia N. Baoulina

We explicitly determine the values of reduced cyclotomic periods of order $2^{m}$ , $m \geq 4$ , for finite fields of characteristic $p \equiv 3$ or $5 (mod 8)$ . These evaluations are app…

math.NT2016

On two problems of Carlitz and their generalizations

Ioulia N. Baoulina

Let $N_{q}$ be the number of solutions to the equation $(a_{1} x_{1}^{m_{1}} + \dots + a_{n} x_{n}^{m_{n}})^{k} = b x_{1}^{k_{1}} \dots x_{n}^{k_{n}}$ over the finite field $F_{q} = F_{p^{s}}$ .…

Integer ratios of consecutive alternating power sums

On the unsolvability of certain equations of Erdős-Moser type

A generalization of the theorems of Chevalley-Warning and Ax-Katz via polynomial substitutions

On a theorem of Morlaye and Joly and its generalization

On period polynomials of degree 2m and weight distributions of certain irreducible cyclic codes

On two problems of Carlitz and their generalizations

On period polynomials of degree $2^{m}$ and weight distributions of certain irreducible cyclic codes