Zobrazeno 1 - 10
of 24
pro vyhledávání: '"Ioulia N. Baoulina"'
Autor:
Ioulia N. Baoulina
Publikováno v:
European Journal of Combinatorics. 80:37-42
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 theorem. Moreover, we extend the result of Morlaye and Joly to the cas
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::51508c25ec58f13c4577f42020413b6f
https://doi.org/10.1016/j.ejc.2018.02.001
https://doi.org/10.1016/j.ejc.2018.02.001
Autor:
Ioulia N. Baoulina
Publikováno v:
The American Mathematical Monthly. 126:651-654
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 consecutive alternating power sums is an integer.
4 pages; to appear
4 pages; to appear
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::85b1faec9bb81c8a7d9ea9f43de09acc
https://doi.org/10.1080/00029890.2019.1606577
https://doi.org/10.1080/00029890.2019.1606577
Publikováno v:
Proceedings of the American Mathematical Society. 147:4107-4122
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 substitution t_i |-> f_i(t_i) for auxiliary polynomials f_1,...,f_n in F_
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4d6a2a41e52effeab6a1feba65b215ae
https://doi.org/10.1090/proc/14181
https://doi.org/10.1090/proc/14181
Autor:
Ioulia N. Baoulina
Publikováno v:
Finite Fields and Their Applications. 50:319-337
We explicitly determine the values of reduced cyclotomic periods of order $2^m$, $m\ge 4$, for finite fields of characteristic $p\equiv 3$ or $5\pmod{8}$. These evaluations are applied to obtain explicit factorizations of the corresponding reduced pe
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b98cd0ac121600f72545a7ea73d20b7b
https://doi.org/10.1016/j.ffa.2017.12.006
https://doi.org/10.1016/j.ffa.2017.12.006
Autor:
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, that for any positive integer $a$, the equation $aS_k(m)=m^k$ has no solu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d450354971087df1a9ab4e7a8bae6652
http://arxiv.org/abs/1804.04646
http://arxiv.org/abs/1804.04646
Autor:
Ioulia N. Baoulina
Publikováno v:
International Journal of Number Theory
In this paper, we use evaluations of Gauss sums modulo pk to derive expressions that allow us for a given generalized Markoff–Hurwitz equation to determine the number of its solutions over ℤ/pkℤ if the number of solutions over ℤ/pℤ is known
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::385397948ab4838f881286547989888c
https://doi.org/10.1142/s1793042115500505
https://doi.org/10.1142/s1793042115500505
Autor:
Ioulia N. Baoulina
Publikováno v:
Topics in Finite Fields. :19-27
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::cbf7d34f4d5b866ef347ad57171151c5
https://doi.org/10.1090/conm/632/12616
https://doi.org/10.1090/conm/632/12616
Publikováno v:
Complex Variables and Elliptic Equations. 60:78-92
We investigate whether certain Diophantine equations have or have not solutions in entire or meromorphic functions defined on a non-Archimedean algebraically closed field of characteristic zero. We prove that there are no non-constant meromorphic fun
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5565c7480a6395f2d0aaf53814daf2c6
https://doi.org/10.1080/17476933.2014.894029
https://doi.org/10.1080/17476933.2014.894029
Autor:
Ioulia N. Baoulina
Publikováno v:
International Journal of Number Theory. 10:421-454
In this paper, using an elementary algebraic-combinatorial approach, we derive expressions that allow us for a given Markoff–Hurwitz equation to find the number of its solutions over ℤ/pkℤ if the number of solutions over ℤ/pℤ is known. We a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0cb4288022ecbbbbbdb0ebb40e617a71
https://doi.org/10.1142/s1793042113501029
https://doi.org/10.1142/s1793042113501029
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 ordering. Shallit himself solved this problem for the set of primes and al
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e5692beb0be08372221c996ab4604d1c
http://arxiv.org/abs/1607.01548
http://arxiv.org/abs/1607.01548