2021
DOI: 10.48550/arxiv.2109.14256
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Lang--Trotter Conjecture for CM Elliptic Curves

Abstract: Notation vii Chapter 1. Backgrounds: history, conjectures and theorems 1.1. Elliptic curves over rationals and finite fields 1.2. Sato-Tate and Lang-Trotter conjectures 1.3. Our main results Chapter 2. The Hardy-Littlewood conjecture and upper bound for π E,r (x) 2.1. The Hardy-Littlewood conjecture and sieve methods 2.2. Elliptic curves with complex multiplication 2.3. Proof of Theorem 1.3 2.4. Fixed trace in imaginary quadratic fields Chapter 3. Power residues and laws of reciprocity 3.1. Quadratic residues … Show more

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