Artin's Primitive Root Conjecture – A Survey
From MaRDI portal
Publication:4902737
DOI10.1515/integers-2012-0043zbMath1271.11002arXivmath/0412262OpenAlexW2963115395WikidataQ123200483 ScholiaQ123200483MaRDI QIDQ4902737
Publication date: 17 January 2013
Published in: Integers (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0412262
Asymptotic results on arithmetic functions (11N37) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Congruences; primitive roots; residue systems (11A07) Density, gaps, topology (11B05)
Related Items (61)
The distribution of rational numbers on Cantor's middle thirds set ⋮ Rational complexity of binary sequences, F\(\mathbb{Q}\)SRs, and pseudo-ultrametric continued fractions in \(\mathbb{R}\) ⋮ Good cyclic codes and the uncertainty principle ⋮ Reductions of algebraic integers ⋮ Bounded gaps between primes with a given primitive root. II ⋮ Several classes of asymptotically good quasi-twisted codes with a low index ⋮ Self-dual and LCD double circulant and double negacirculant codes over \({\mathbb{F}}_q+u{\mathbb{F}}_q+v{\mathbb{F}}_q\) ⋮ Average $r$-rank Artin conjecture ⋮ Continuant, Chebyshev polynomials, and Riley polynomials ⋮ EXPLICIT KUMMER THEORY FOR QUADRATIC FIELDS ⋮ Self-dual and LCD double circulant codes over a class of non-local rings ⋮ On the distribution of the order and index for the reductions of algebraic numbers ⋮ ON LINEAR COMPLEMENTARY DUAL FOUR CIRCULANT CODES ⋮ Moser's mathemagical work on the equation \(1^k+2^k+\ldots+(m-1)^k=m^k\) ⋮ An analogue of Artin's conjecture for multiplicative subgroups of the rationals ⋮ On self-dual and LCD double circulant and double negacirculant codes over \(\mathbb{F}_q+u\mathbb{F}_q \) ⋮ Asymptotic performance of metacyclic codes ⋮ Large absolute values of cyclotomic polynomials at roots of unity ⋮ Divisibility conditions on the order of the reductions of algebraic numbers ⋮ Unified treatment of Artin-type problems ⋮ Positive lower density for prime divisors of generic linear recurrences ⋮ Multi-twisted additive codes over finite fields are asymptotically good ⋮ Algebraic algorithms for variants of subset sum ⋮ Comparing balanced sequences obtained from ElGamal function to random balanced sequences ⋮ Salajan's conjecture on discriminating terms in an exponential sequence ⋮ Prime divisors of \(\ell\)-Genocchi numbers and the ubiquity of Ramanujan-style congruences of level \(\ell\) ⋮ ON THE MINIMAL NUMBER OF SMALL ELEMENTS GENERATING FINITE PRIME FIELDS ⋮ On the order modulo p of an algebraic number ⋮ Extremal hypercuts and shadows of simplicial complexes ⋮ Double Circulant Self-Dual and LCD Codes Over ℤp2 ⋮ On Self-Dual Four Circulant Codes ⋮ Strong Skolem starters ⋮ LOWER BOUNDS FOR PERIODS OF DUCCI SEQUENCES ⋮ The order of the reductions of an algebraic integer ⋮ Primes, elliptic curves and cyclic groups ⋮ Multiplicative Order and Frobenius Symbol for the Reductions of Number Fields ⋮ Low-degree factors of random polynomials ⋮ Probabilistic study of Fermats quotients ⋮ Irreducibility of Random Polynomials ⋮ Periodic binary harmonic functions on lattices ⋮ On self-dual double circulant codes ⋮ Browkin’s discriminator conjecture ⋮ On Grosswald’s conjecture on primitive roots ⋮ Long quasi-polycyclic \(t\)-CIS codes ⋮ On self-dual double negacirculant codes ⋮ A lower bound for the two-variable Artin conjecture and prime divisors of recurrence sequences ⋮ Vinogradov’s three primes theorem with primes having given primitive roots ⋮ Generalized Artin Primitive Root Conjecture ⋮ REDUCTIONS OF POINTS ON ALGEBRAIC GROUPS ⋮ A modified Gilbert-Varshamov bound for self-dual quasi-twisted codes of index four ⋮ On self-dual and LCD quasi-twisted codes of index two over a special chain ring ⋮ On the density of irreducible polynomials which generate \(k\)-free polynomials over function fields ⋮ Kummer theory for number fields and the reductions of algebraic numbers ⋮ The average multiplicative order of a finitely generated subgroup of the rationals modulo primes ⋮ Irregular primes with respect to Genocchi numbers and Artin's primitive root conjecture ⋮ Periodic harmonic functions on lattices and points count in positive characteristic ⋮ Divisibility of reduction in groups of rational numbers ⋮ PRIMES IN ARITHMETIC PROGRESSIONS AND NONPRIMITIVE ROOTS ⋮ On the stability of periodic binary sequences with zone restriction ⋮ Equality of orders of a set of integers modulo a prime ⋮ On the Average Value of a Function of the Residual Index
This page was built for publication: Artin's Primitive Root Conjecture – A Survey