Short Proofs for Nondivisibility of Sparse Polynomials under the Extended Riemann Hypothesis

1996 ◽  
Vol 28 (3,4) ◽  
pp. 297-301 ◽  
Author(s):  
Dima Grigoriev ◽  
Marek Karpinski ◽  
Andrew M. Odlyzko
Author(s):  
N. P. Prochorov

In this paper, we obtained the primality criteria for ideals of rings of integer algebraic elements of finite extensions of the field Q, which are analogues of Miller and Euler’s primality criteria for rings of integers. Also advanced analogues of these criteria were obtained, assuming the extended Riemann hypothesis. Arithmetic and modular operations for ideals of rings of integer algebraic elements of finite extensions of the field Q were elaborated. Using these criteria, the polynomial probabilistic and deterministic algorithms for the primality testing in rings of integer algebraic elements of finite extensions of the field Q were offered.


Mathematika ◽  
2016 ◽  
Vol 63 (1) ◽  
pp. 29-33 ◽  
Author(s):  
Sandro Bettin ◽  
Steven M. Gonek
Keyword(s):  

Sign in / Sign up

Export Citation Format

Share Document