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An analogue of the Siegel-Walfisz theorem for the cyclicity of CM elliptic curves mod p

Author

Listed:
  • Amir Akbary

    (University of Lethbridge)

  • V. Kumar Murty

    (University of Toronto)

Abstract

Let E be a CM elliptic curve defined over ℚ and of conductor N. We establish an asymptotic formula, uniform in N and with improved error term, for the counting function of primes p for which the reduction mod p of E is cyclic. Our result resembles the classical Siegel-Walfisz theorem regarding the distribution of primes in arithmetic progressions.

Suggested Citation

  • Amir Akbary & V. Kumar Murty, 2010. "An analogue of the Siegel-Walfisz theorem for the cyclicity of CM elliptic curves mod p," Indian Journal of Pure and Applied Mathematics, Springer, vol. 41(1), pages 25-37, February.
    • Handle: RePEc:spr:indpam:v:41:y:2010:i:1:d:10.1007_s13226-010-0002-4
    DOI: 10.1007/s13226-010-0002-4
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