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ON THE DISTRIBUTION OF TORSION POINTS MODULO PRIMES

Part of: Algebraic number theory: global fields Arithmetic algebraic geometry Multiplicative number theory

Published online by Cambridge University Press:  16 February 2012

YEN-MEI J. CHEN  and
YEN-LIANG KUAN
YEN-MEI J. CHEN*
Affiliation:
Department of Mathematics, National Central University, Jhongli City, Taoyuan County 32001, Taiwan (email: ymjchen@math.ncu.edu.tw)
YEN-LIANG KUAN
Affiliation:
Department of Mathematics, National Central University, Jhongli City, Taoyuan County 32001, Taiwan (email: 952201001@cc.ncu.edu.tw)
*
✉For correspondence; e-mail: ymjchen@math.ncu.edu.tw
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Abstract

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Let be a commutative algebraic group defined over a number field K. For a prime ℘ in K where has good reduction, let N℘,n be the number of n-torsion points of the reduction of modulo ℘ where n is a positive integer. When is of dimension one and n is relatively prime to a fixed finite set of primes depending on , we determine the average values of N℘,n as the prime ℘ varies. This average value as a function of n always agrees with a divisor function.

Keywords

number fieldsalgebraic groupstorsion pointselliptic curvescomplex multiplication

MSC classification

Secondary: 11N13: Primes in progressions 11R18: Cyclotomic extensions 11G05: Elliptic curves over global fields
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 2 , October 2012 , pp. 339 - 347
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

Footnotes

Research partially supported by National Science Council, Republic of China.

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