Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Elliptic pseudoprimes
HTML articles powered by AMS MathViewer

by I. Miyamoto and M. Ram Murty PDF
Math. Comp. 53 (1989), 415-430 Request permission


Let E be an elliptic curve over Q with complex multiplication by an order in an imaginary quadratic field. Let ${\psi _n}$ denote the nth division polynomial, and let P be a rational point of E of infinite order. A natural number n is called an elliptic pseudoprime if $n|{\psi _{n + 1}}(P)$ and n is composite. Let $N(x)$ denote the number of elliptic pseudoprimes up to x. We show that $N(x) \ll x{(\log \log x)^{7/2}}/{(\log x)^{3/2}}$. More generally, if ${P_1}, \ldots ,{P_r}$ are r independent rational points of E which have infinite order, and $\Gamma$ is the subgroup generated by them, denote by ${N_\Gamma }(x)$ the number of composite $n \leq x$ satisfying $n|{\psi _{n + 1}}({P_i})$, $1 \leq i \leq r$. For $r \geq 2$, we prove ${N_\Gamma }(x) \ll x\exp ( - c\sqrt {(\log x)(\log \log x))}$ for some positive constant c.
Similar Articles
Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 53 (1989), 415-430
  • MSC: Primary 11G05; Secondary 11A51, 11Y11
  • DOI:
  • MathSciNet review: 970701