Igor E. Shparlinski

1. Additive Decompositions of Subgroups of Finite Fields
   2013/01/14 by Igor E. Shparlinski, Shparlinski, Igor · 3 citations
   Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #graph theory and CDMA systems
2. On The Solvability of Bilinear Equations in Finite Fields
   2007/08/16 by Igor E. Shparlinski, Shparlinski, Igor E. · 3 citations
   Computer Science · Mathematics · #11L40 #11T30 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories
3. Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices
   2022/03/08 by Alina Ostafe, Habegger, Philipp, Igor E. Shparlinski +2 · 3 citations
   Mathematics · Computer Science · #Finite Group Theory Research #Coding theory and cryptography #Advanced Algebra and Geometry
4. On vanishing Fermat quotients and a bound of the Ihara sum
   2011/04/20 by Igor E. Shparlinski, Shparlinski, Igor E. · 2 citations
   Mathematics · Computer Science · #Analytic Number Theory Research #Algebraic Geometry and Number Theory #Coding theory and cryptography
5. Bounds on bilinear forms with Kloosterman sums
   2022/04/11 by Bryce Kerr, Kerr, Bryce, Igor E. Shparlinski +5 · 3 citations
   Mathematics · #Analytic Number Theory Research
6. Short Cycles in Repeated Exponentiation Modulo a Prime
   2009/08/27 by Lev Glebsky, Glebsky, Lev, Igor E. Shparlinski +1 · 1 citation
   Computer Science · #11A07 #Chaos-based Image/Signal Encryption #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)
7. On group structures realized by elliptic curves over arbitrary finite\n fields
   2010/03/15 by William D. Banks, Banks, William D., Francesco Pappalardi +3 · 1 citation
   Computer Science · Mathematics · #11G05 #14H52 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)
8. On group structures realized by elliptic curves over a fixed finite field
   2010/03/15 by Reza Rezaeian Farashahi, Farashahi, Reza Rezaeian, Igor E. Shparlinski +1 · 1 citation
   Computer Science · Mathematics · #11G05 #14H52 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)
9. On the Typical Size and Cancelations Among the Coefficients of Some Modular Forms
   2013/08/29 by Florian Luca, Maksym Radziwiłł, Luca, Florian +3 · 1 citation
   Mathematics · #Analytic Number Theory Research #Advanced Algebra and Geometry #Advanced Mathematical Identities
10. Functional Graphs of Polynomials over Finite Fields
    2013/07/10 by Sergeĭ Konyagin, Konyagin, Sergei V., Florian Luca +9 · 1 citation
    Computer Science · Mathematics · #05C20 #05C85 #11T06 #11T24 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT)
11. Polynomial Interpolation and Identity Testing from High Powers over\n Finite Fields
    2015/02/23 by Gábor Ivanyos, Ivanyos, Gabor, Marek Karpiński +7 · 1 citation
    Computer Science · #Cryptography and Data Security #Cryptography and Residue Arithmetic #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT) #Quantum Computing Algorithms and Architecture
12. Counting Co-Cyclic Lattices
    2015/05/24 by Phong Q. Nguyễn, Igor E. Shparlinski, Nguyen, Phong Q. +1 · 1 citation
    Computer Science · #semigroups and automata theory #Advanced Algebra and Logic #Advanced Graph Theory Research
13. On some matrix counting problems
    2023/10/08 by Ali Mohammadi, Mohammadi, Ali, Alina Ostafe +3 · 2 citations
    Mathematics · Engineering · Computer Science · #Graph theory and applications #graph theory and CDMA systems #Matrix Theory and Algorithms
14. Discriminants of Fields Generated by Polynomials of Given Height
    2019/08/31 by Rainer Dietmann, Dietmann, Rainer, Alina Ostafe +3 · 1 citation
    Computer Science · Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #Tensor decomposition and applications
15. Weyl sums over integers with digital restrictions
    2021/05/11 by Igor E. Shparlinski, Shparlinski, Igor E., Jörg Μ. Thuswaldner +1 · 1 citation
    Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT)
16. Exponential Sums and Congruences with Factorials
    2004/03/24 by Moubariz Z. Garaev, Florian Luca, Garaev, Moubariz Z. +3 · 1 citation
    Mathematics · #11A07 #11B65 #11L40 #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #math.CO #math.NT #msc:11A07 #msc:11B65 #msc:11L40
17. Character Sums and Congruences with n!
    2004/03/24 by Moubariz Z. Garaev, Garaev, Moubariz Z., Florian Luca +3 · 1 citation
    Mathematics · #11A07 #11B65 #11L40 #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #math.CO #math.NT #msc:11A07 #msc:11B65 #msc:11L40
18. Pseudorandom Numbers and Hash Functions from Iterations of Multivariate\n Polynomials
    2009/08/31 by Alina Ostafe, Igor E. Shparlinski, Ostafe, Alina +1 · 1 citation
    Computer Science · #11K45 #11T23 #11T71 #94A60 #Chaos-based Image/Signal Encryption #Coding theory and cryptography #Cryptography and Residue Arithmetic #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation
19. Character sums over sparse elements of finite fields
    2022/11/15 by László Mérai, Mérai, László, Igor E. Shparlinski +3 · 1 citation
    Computer Science · Mathematics · #Coding theory and cryptography #Cryptography and Residue Arithmetic #Finite Group Theory Research
20. Multiplicative Congruences with Variables from Short Intervals
    2012/10/24 by Jean Bourgain, Moubariz Z. Garaev, Bourgain, Jean +5 · 1 citation
    Mathematics · #11A07 #11D79 #11N25 #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT)
21. Rational numbers with small denominators in short intervals
    2023/11/28 by Igor E. Shparlinski, Shparlinski, Igor E. · 1 citation
    Computer Science · Mathematics · #Analytic Number Theory Research #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)
22. On the sparsity of non-diagonalisable integer matrices and matrices with a given discriminant
    2023/12/19 by Alina Ostafe, Ostafe, Alina, Igor E. Shparlinski +1 · 1 citation
    Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Graph theory and applications #Number Theory (math.NT) #Point processes and geometric inequalities
23. Distribution of recursive matrix pseudorandom number generator modulo prime powers
    2023/02/08 by László Mérai, Mérai, László, Igor E. Shparlinski +1 · 2 citations
    Computer Science · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories
24. Sums of Kloosterman sums over square-free and smooth integers
    2024/11/18 by Xuancheng Shao, Shao, Xuancheng, Igor E. Shparlinski +3 · 1 citation
    Mathematics · Computer Science · #Analytic Number Theory Research #Limits and Structures in Graph Theory #Coding theory and cryptography
25. Points on curves in small boxes en applications
    2011/11/07 by Mei-Chu Chang, Chang, Mei-Chu, Javier Cilleruelo +9 · 1 citation
    Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)
26. Counting matrices over finite rank multiplicative groups
    2025/02/10 by Aaron Manning, Manning, Aaron, Alina Ostafe +3 · 1 citation
    Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT