Ioulia N. Baoulina

activity

20152018

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

4 citations · 16 across the 11 of their papers we have counts for

collaborators

11 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★ 1 cited

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★ 4 cited

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★ 1 cited

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★ 1 cited

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 $F_{q} = F_{p^{s}}$ .…

math.NT2016★ 2 cited

Deleting digits

Ioulia N. Baoulina, Martin Kreh, Jörn Steuding

In 2000, J. Shallit introduced a special partial ordering of a subset of positive integers and proposed the problem of finding the set of minimal elements with respect to this orde…

math.NT2016

On period polynomials of degree $2^{m}$ for finite fields

Ioulia N. Baoulina

We obtain explicit factorizations of reduced period polynomials of degree $2^{m}$ , $m \geq 4$ , for finite fields of characteristic $p \equiv 3$ or $5 (mod 8)$ . This extends the results…

math.NT2016★ 3 cited

On a class of diagonal equations over finite fields

Ioulia N. Baoulina

Using properties of Gauss and Jacobi sums, we derive explicit formulas for the number of solutions to a diagonal equation of the form $x_{1}^{2^{m}} + \dots + x_{n}^{2^{m}} = 0$ over a finite fi…

math.NT2015★ 2 cited

Forbidden integer ratios of consecutive power sums

Ioulia N. Baoulina, Pieter Moree

Let $S_{k} (m) := 1^{k} + 2^{k} + \dots + (m - 1)^{k}$ denote a power sum. In 2011 Bernd Kellner formulated the conjecture that for $m \geq 4$ the ratio $S_{k} (m + 1) / S_{k} (m)$ of two consecutive power sums…

math.NT2015★ 2 cited

Solutions of equations over finite fields: enumeration via bijections

Ioulia N. Baoulina

We present a simple proof of the well-known fact concerning the number of solutions of diagonal equations over finite fields. In a similar manner, we give an alternative proof of t…

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

Deleting digits

On period polynomials of degree 2m for finite fields

On a class of diagonal equations over finite fields

Forbidden integer ratios of consecutive power sums

Solutions of equations over finite fields: enumeration via bijections

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

On period polynomials of degree $2^{m}$ for finite fields