Average root numbers

in families of elliptic curves

Author:
Ottavio G. Rizzo

Journal:
Proc. Amer. Math. Soc. **127** (1999), 1597-1603

MSC (1991):
Primary 11G05; Secondary 11D25, 11C08, 28C10

DOI:
https://doi.org/10.1090/S0002-9939-99-05167-9

Published electronically:
February 18, 1999

MathSciNet review:
1641093

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We introduce a height measure on to count rational numbers. Through it, we prove a density result on the average value of the root numbers of families of twists of elliptic curves.

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Additional Information

**Ottavio G. Rizzo**

Affiliation:
Department of Mathematics, Brown University, Box 1917, Providence, Rhode Island 02912

Address at time of publication:
Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada K7L 3N6

Email:
otto@math.brown.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-05167-9

Received by editor(s):
September 15, 1997

Published electronically:
February 18, 1999

Additional Notes:
This research was partially written while the author was supported by a grant of the Istituto Nazionale di Alta Matematica of Rome.

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 1999
American Mathematical Society