Computer verification of the Ankeny--Artin--Chowla Conjecture for all primes less than $100000000000$
From MaRDI portal
Publication:2719083
DOI10.1090/S0025-5718-00-01234-5zbMath0987.11065OpenAlexW2150932406MaRDI QIDQ2719083
Alfred J. van der Poorten, Herman J. J. te Riele, Hugh C. Williams
Publication date: 14 May 2001
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0025-5718-00-01234-5
Quadratic extensions (11R11) Continued fractions and generalizations (11J70) Algebraic number theory computations (11Y40) Continued fractions (11A55) Software, source code, etc. for problems pertaining to number theory (11-04) Continued fraction calculations (number-theoretic aspects) (11Y65)
Related Items
New Computations Concerning the Cohen-Lenstra Heuristics ⋮ On Yokoi’s Invariants and the Ankeny–Artin–Chowla conjecture ⋮ Direct-sum cancellation for modules over real quadratic orders ⋮ Approximating Euler products and class number computation in algebraic function fields ⋮ Wolstenholme and Vandiver primes ⋮ An Adaptation of the NICE Cryptosystem to Real Quadratic Orders ⋮ Ankeny-Artin-Chowla and Mordell conjectures in terms of \(p\)-rationality ⋮ On the odd prime solutions of the Diophantine equation \(x^y + y^x = z^z\) ⋮ New bounds for the fundamental units and class numbers of real quadratic fields ⋮ Unnamed Item ⋮ The exponential diophantine equation xy + yx = z2 via a generalization of the Ankeny–Artin–Chowla conjecture ⋮ A fast, rigorous technique for computing the regulator of a real quadratic field ⋮ Ankeny-Artin-Chowla conjecture and continued fraction expansion ⋮ Unnamed Item ⋮ A new condition equivalent to the Ankeny-Artin-Chowla conjecture ⋮ On a conjecture of Mordell ⋮ Complete solution of the Diophantine equation $x^y+y^x=z^z$ ⋮ Integer points and independent points on the elliptic curve \(y^2=x^3-p^kx\) ⋮ Life and Mathematics of Alfred Jacobus van der Poorten (1942–2010) ⋮ Counterexamples to the local-global principle for non-singular plane curves and a cubic analogue of Ankeny-Artin-Chowla-Mordell conjecture ⋮ The Diophantine equation $x^p+1=py^2$
Cites Work
- The class-number of real quadratic number fields
- A note on the class number of real quadratic fields
- On a Pellian equation conjecture
- Some Computational Results on a Problem Concerning Powerful Numbers
- Multiplication modulon
- Faster computation of Bernoulli numbers
- On the Parallel Generation of the Residues for the Continued Fraction Factoring Algorithm
- A further note on the class number of real quadratic fields
- A search for Wieferich and Wilson primes
- On a Pellian Equation Conjecture (II)
- The Class-Number of Real Quadratic Fields
- Note on the Class Number of Real Quadratic Fields
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
