Abstract
Let A an abelian variety of dimension r, defined over Q. For p a rational prime, we denote by Fp the finite field of cardinality p. If A has good reduction at p, let A¯p be the reduction of A at p. Let Γ be a free subgroup of the Mordell–Weil group A(Q), and let Γp be the reduction of Γ at p. In this paper for abelian varieties of type I, II, III, and IV, under Generalized Riemann Hypothesis, Artin's Holomorphy Conjecture, and Pair Correlation Conjecture, we obtain asymptotic formulas for the number of primes p, with p≤x, for which the quotient [Formula presented] has at most 2r−1 cyclic components.
Original language | English |
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Pages (from-to) | 135-144 |
Number of pages | 10 |
Journal | Journal of Number Theory |
Volume | 197 |
DOIs | |
Publication status | Published - 2019 Apr |
Bibliographical note
Funding Information:This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2015R1D1A1A01056643).
Publisher Copyright:
© 2018 Elsevier Inc.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory