I. N. Baoulina, A. Bishnoi, P. L. Clark, “A generalization of the theorems of Chevalley-Warning and Ax-Katz via polynomial substitutions”, Proc. Amer. Math. Soc., 147:10 (2019), 4107–4122 , arXiv: 1709.05699
I. N. Baoulina, “Integer ratios of consecutive alternating power sums”, Amer. Math. Monthly, 126:7 (2019), 651–654 , arXiv: 1809.03365
I. N. Baoulina, “On period polynomials of degree $2^m$ and weight distributions of certain irreducible cyclic codes”, Finite Fields Appl., 50 (2018), 319–337 , arXiv: 1703.09204
I. N. Baoulina, “On a class of diagonal equations over finite fields”, Finite Fields Appl., 40 (2016), 201–223 , arXiv: 1602.01807
I. N. Baoulina, P. Moree, “Forbidden integer ratios of consecutive power sums”, From Arithmetic to Zeta-Functions: Number Theory in Memory of Wolfgang Schwarz, eds. J. Sander, J. Steuding, R. Steuding, Springer International Publishing, 2016, 1–30https://arxiv.org/abs/1510.06064
I. N. Baoulina, A. Bishnoi, P. L. Clark, “A generalization of the theorems of Chevalley-Warning and Ax-Katz via polynomial substitutions”, Proc. Amer. Math. Soc., 147:10 (2019), 4107–4122 , arXiv: 1709.05699
I. N. Baoulina, “Integer ratios of consecutive alternating power sums”, Amer. Math. Monthly, 126:7 (2019), 651–654 , arXiv: 1809.03365
5.
I. N. Baoulina, “On period polynomials of degree $2^m$ and weight distributions of certain irreducible cyclic codes”, Finite Fields Appl., 50 (2018), 319–337 , arXiv: 1703.09204
I. N. Baoulina, A. Bishnoi, P. L. Clark, “On a generalization of the theorems of Chevalley-Warning and Ax-Katz”, Materialy XV Mezhdunarodnoi konferentsii "Algebra, teoriya chisel i diskretnaya geometriya: sovremennye problemy i prilozheniya, posvyaschennoi stoletiyu so dnya rozhdeniya doktora fiziko-matematicheskikh nauk, professora Moskovskogo gosudarstvennogo universiteta imeni M. V. Lomonosova Korobova Nikolaya Mikhailovicha (Tula, 28-31 maya 2018 goda), TGPU im. L. N. Tolstogo, Tula, 2018, 203–205
7.
I. N. Baoulina, M. Kreh, J. Steuding, “Deleting digits”, Math. Gaz., 101:550 (2017), 60–68 , arXiv: 1607.01548
I. N. Baoulina, “On two problems of Carlitz and their generalizations”, Finite Fields: Theory, Fundamental Properties and Applications, Mathematics Research Developments, eds. J. Simmons, Nova Science Publishers, 2017, 147–159https://arxiv.org/abs/1609.04807
9.
I. N. Baoulina, “Solutions of equations over finite fields: Enumeration via bijections”, J. Algebra Appl., 15:7 (2016), 1650136 , 6 pp., arXiv: 1505.07941
I. N. Baoulina, P. Moree, “Forbidden integer ratios of consecutive power sums”, From Arithmetic to Zeta-Functions: Number Theory in Memory of Wolfgang Schwarz, eds. J. Sander, J. Steuding, R. Steuding, Springer International Publishing, 2016, 1–30https://arxiv.org/abs/1510.06064
I. N. Baoulina, “On the solvability of certain equations over finite fields”, Topics in finite fields, Contemp. Math., 632, eds. G. Kyureghyan, G. L. Mullen, A. Pott, Amer. Math. Soc., Providence, RI, 2015, 19–27
16.
I. N. Baoulina, P. Moree, “On the Kellner-Erdős-Moser equation”, Algebra, teoriya chisel i diskretnaya geometriya: sovremennye problemy i prilozheniya (Tula, 25–30 maya 2015 g.), TGPU im. L. N. Tolstogo, Tula, 2015, 209–211
17.
I. N. Baoulina, “On Markoff–Hurwitz equations over residue class rings”, Int. J. Number Theory, 10:2 (2014), 421–454
I. N. Baoulina, “On the Carlitz problem on the number of solutions to some special equations over finite fields”, J. Théor. Nombres Bordeaux, 23:1 (2011), 1–20
19.
I. Baoulina, “On the number of solutions to certain diagonal equations over finite fields”, Int. J. Number Theory, 6:1 (2010), 1–14
I. Baoulina, “On the number of solutions to the equation $(x_1 +\dots+x_n)^m =ax_1\cdots x_n$ over the finite field $\mathbb F_q$ for $\gcd(m-n,q-1)=7$ and for $\gcd(m-n,q-1)=14$”, Number Theory and Applications: Proceedings of the International Conferences on Number Theory and Cryptography, eds. S. D. Adhikari, B. Ramakrishnan, Hindustan Book Agency, New Delhi, 2009, 15–24
I. Baoulina, “On the number of solutions to the equation $(x_1+\dots+ x_n)^2=ax_1\cdots x_n$ in a finite field”, Int. J. Number Theory, 4:5 (2008), 797–817
I. Baoulina, “On the number of solutions of the equation $a_1^{\vphantom{m_1}}x_1^{m_1}+\dots+a_n^{\vphantom{m_n}}x_n^{m_n}=bx_1\cdots x_n$ in a finite field”, Acta Appl. Math., 85:1 (2005), 35–39
Yu. N. Baulina, “On the number of solutions of the equation $(x_1+\dots+x_n)^m=ax_1\cdots x_n$ in a finite field”, Discrete Math. Appl., 14:5 (2004), 501–508
31.
Yu. N. Baulina, “On explicit formulas for the number of solutions to the equation $(x_1+\dots+x_n)^2=ax_1\cdots x_n$ in a finite field”, Siberian Math. J., 44:1 (2003), 17–21
32.
I. Baoulina, “On the problem of explicit evaluation of the number of solutions of the equation $a_1^{\vphantom{2}} x_1^2 +\dots+a_n^{\vphantom{2}} x_n^2 =bx_1\cdots x_n$ in a finite field”, Current Trends in Number Theory, eds. S. D. Adhikari, S. A. Katre, B. Ramakrishnan, Hindustan Book Agency, New Delhi, 2002, 27–37
Yu. N. Baulina, “On the number of solutions of the equation $(x_1+\dots+x_n)^2=ax_1\cdots x_n$ in the finite field $\mathbb F_q$ for $\mathrm{gcd}(n-2,q-1)=7$ and for $\mathrm{gcd}(n-2,q-1)=14$”, Chebyshevskii Sb., 1:1 (2001), 5–14
34.
Yu. N. Baulina, “On exact values of some trigonometric sums in finite fields”, Scientific Transactions of the Department of Mathematics of Moscow State Pedagogical University: Jubilee collected articles 100 years, Prometey, Moscow, 2001, 218–223
35.
Yu. N. Baulina, “On the exact formulas for the number of solutions to the equation $a_1x_1^2+\dots+a_nx_n^2=mx_1\cdots x_n$ in a finite field”, Universal Algebra and Its Applications, Transactions of the International Seminar, dedicated to the memory of Prof. L. A. Skornyakov (September 6–11, 1999, Volgograd, Russia), Peremena, Volgograd, 2000, 29–33
36.
Yu. N. Baulina, “On the solution of the generalized Markov equation”, Math. Notes, 59:3 (1996), 320–321
37.
Yu. N. Baulina, “On the number of solutions to the Diophantine equation $x_1^2+\dots+x_n^2+ax_1+\dots+ax_n+b=(an+b+n)x_1\cdots x_n$ below a given bound”, Transactions of the Moscow Lenin State Pedagogical University, Ser. Natural Sciences, Prometey, Moscow, 1996, 9–11
38.
Yu. N. Baulina, “On the number of solutions of the equation $x_1^2+\dots+x_n^2=nx_1\cdots x_n$, not exceeding a given limit”, Math. Notes, 57:2 (1995), 208–210
39.
Yu. N. Baulina, “The Diophantine equation $x_1^2+\dots+x_n^2+mx_{n+1}^2=mx_1\cdots x_n x_{n+1}$”, Theoretical and applied aspects of mathematical investigations, eds. O. B. Lupanov, Moscow State University, Moscow, 1994, 40–43
40.
Yu. N. Baulina, “Fundamental solutions of the equation $x_1^2+\dots+x_n^2=mx_1\cdots x_n$”, Math. Notes, 52:5 (1992), 1168–1169
41.
V. N. Chubarikov, V. G. Chirskii, E. Deza, I. N. Baoulina, L. V. Kotova, E. V. Neiskashova, V. S. Vankova, N. M. Dobrovolskii, I. Yu. Rebrova, A. L. Roshchenya, “Vassiliy Ilyich Nechaev. To the 100-th anniversary”, Chebyshevskii Sb., 21:1 (2020), 383–393
42.
I. N. Baoulina, M. Kreh, J. Steuding, “Feedback on 'Deleting Digits'”, Math. Gaz., 101:551 (2017), 337–338
43.
M. P. Mineev, V. N. Chubarikov, V. G. Chirskii, A. V. Gmuleva, E. I. Deza, I. N. Baoulina, V. S. Van'kova, N. M. Dobrovol'skii, I. Yu. Rebrova, A. L. Roshchenya, “The 95th anniversary of Vassiliy Ilyich Nechaev”, Chebyshevskii Sb., 16:1 (2015), 317–331
Presentations in Math-Net.Ru
1.
On a generalization of the theorems of Chevalley–Warning and Ax–Katz I. N. Baoulina XV International Conference «Algebra, Number Theory and Discrete Geometry: modern problems and applications», dedicated to the centenary of the birth of the Doctor of Physical and Mathematical Sciences, Professor of the Moscow State University Korobov Nikolai Mikhailovich May 29, 2018 16:30
