AN ANALOGUE OF THE SIEGEL-WALFISZ THEOREM FOR THE CYCLICITY OF CM ELLIPTIC CURVES MOD p

作者：Akbary Amir^*; Murty V Kumar

来源：Indian Journal of Pure and Applied Mathematics, 2010, 41(1): 25-37.

DOI：10.1007/s13226-010-0002-4

• Reduction mod p of elliptic curves
• cyclicity of CM elliptic curves mod p
• Siegel-Walfisz Theorem

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.

• 出版日期2010-2