Subgroups generated by rational functions in finite fields

DOI10.1007/s00605-014-0697-0zbMath1395.11071arXiv1309.7378OpenAlexW2109069877MaRDI QIDQ2255262

Igor E. Shparlinski, Domingo Gómez-Pérez

Publication date: 9 February 2015

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.7378

zbMATH Keywords

finite fieldsmultiplicative subgroupspolynomial congruencesvalue sets of polynomials

Mathematics Subject Classification ID

Polynomials over finite fields (11T06) Congruences in many variables (11D79)

Related Items (5)

Polynomial interpolation and identity testing from high powers over finite fields ⋮ Identity testing and interpolation from high powers of polynomials of large degree over finite fields ⋮ SYSTEMS OF CONGRUENCES WITH PRODUCTS OF VARIABLES FROM SHORT INTERVALS ⋮ Values of rational functions in small subgroups of finite fields and the identity testing problem from powers ⋮ A probabilistic analysis on a lattice attack against DSA

Cites Work

• Unnamed Item
• Unnamed Item
• Elements of large order on varieties over prime finite fields
• Order of Gauss periods in large characteristic
• Vinogradov's mean value theorem via efficient congruencing
• Elements of high order in finite fields of the form
• Points on curves in small boxes and applications
• On the distribution of the residues of small multiplicative subgroups of \(\mathbb F_p\)
• Reducibility of rational functions in several variables
• Finite field elements of high order arising from modular curves
• Geometric algorithms and combinatorial optimization.
• Reducibility of polynomials in two variables
• On the concentration of points of polynomial maps and applications
• Elements of high order in finite fields of the form \(\mathbb F_q[x/(x^m-a)\)]
• Vinogradov's mean value theorem via efficient congruencing. II
• Multiplicative congruences with variables from short intervals
• Isomorphism classes of elliptic curves over a finite field in some thin families
• The number of integral points on arcs and ovals
• ELEMENTS OF LARGE ORDER IN PRIME FINITE FIELDS
• SOLUTIONS TO POLYNOMIAL CONGRUENCES IN WELL-SHAPED SETS
• Multigrade efficient congruencing and Vinogradov's mean value theorem
• ELEMENTS OF HIGH ORDER ON FINITE FIELDS FROM ELLIPTIC CURVES
• On the Hidden Shifted Power Problem
• Groups generated by iterations of polynomials over finite fields

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