On the refined Koblitz conjecture

Authors

• Sampa Dey, Indian Statistical Institute, Kolkata
• Arnab Saha, Indian Institute of Technology Gandhinagar
• Jyothsnaa Sivaraman, Indian Institute of Science Education and Research Thiruvananthapuram
• Akshaa Vatwani, Indian Institute of Technology Gandhinagar

Article Type

Research Article

Publication Title

Journal of Mathematical Analysis and Applications

Abstract

Let p be a prime, E be a non-CM elliptic curve over Q, and Np be the number of points of E over Fp. Given t∈N, we are concerned with the asymptotic formula for the set of primes for which Np/t is a prime. The asymptotic constant was first conjectured by Koblitz for t=1 and the conjecture was later refined by Zywina. Assuming an elliptic analogue of the Elliott-Halberstam conjecture and a conjecture on the average order of growth of Np, this paper arrives at the conjectured constant, using techniques from classical analytic number theory. This is the first result where the conjectured constant is conditionally determined.

DOI

10.1016/j.jmaa.2024.129212

Publication Date

6-1-2025

Recommended Citation

Dey, Sampa; Saha, Arnab; Sivaraman, Jyothsnaa; and Vatwani, Akshaa, "On the refined Koblitz conjecture" (2025). Journal Articles. 5504.
https://digitalcommons.isical.ac.in/journal-articles/5504