On the Mertens Conjecture for Elliptic Curves over Finite Fields

Abstract

We introduce an analogue of the Mertens conjecture for elliptic curves over finite fields. Using a result of Waterhouse, we classify the isogeny classes of elliptic curves for which this conjecture holds in terms the size of the finite field and the trace of the Frobenius endomorphism acting on the curve.

12 pages. Minor revisions and additional references added. To appear in Bulletin of the Australian Mathematical Society

References in corpus (2)

• On the Mertens Conjecture for Function Fields
• The summatory function of the Möbius function in function fields

Cited by in corpus (1)

• An annotated bibliography for comparative prime number theory