ELEMENTS OF LARGE ORDER IN PRIME FINITE FIELDS

DOI10.1017/S0004972712000810zbMath1300.11017MaRDI QIDQ2847608

Mei-Chu Chang

Publication date: 11 September 2013

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

finite fieldsmultiplicative orderadditive combinatoricsmultiplicative group

Mathematics Subject Classification ID

Other combinatorial number theory (11B75) Arithmetic theory of polynomial rings over finite fields (11T55) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (10)

High order elements in finite fields arising from recursive towers ⋮ Arithmetic and dynamics on varieties of Markoff type ⋮ Markoff triples and strong approximation ⋮ Polynomial values in small subgroups of finite fields ⋮ Multiplicative congruences with variables from short intervals ⋮ Subgroups generated by rational functions in finite fields ⋮ On periods modulo \(p\) in arithmetic dynamics ⋮ Orders of points in families of elliptic curves ⋮ Order of torsion for reduction of linearly independent points for a family of Drinfeld modules ⋮ Elements of large order on varieties over prime finite fields

Cites Work

• On the maximal order of a torsion point on a curve in \(\mathbb{G}^n_m\)
• An upper bound for the g.c.d. of \(a^n-1\) and \(b^n -1\)
• Sharp estimates for the arithmetic Nullstellensatz
• On sums of roots of unity
• The distribution of integers with a divisor in a given interval
• ELEMENTS OF HIGH ORDER ON FINITE FIELDS FROM ELLIPTIC CURVES
• Torsion points on curves and common divisors of a^k-1 and b^k-1
• On the multiplicative orders of \(\gamma\) and \(\gamma+\gamma^{-1}\) over finite fields

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