Order of torsion for reduction of linearly independent points for a family of Drinfeld modules
| Autor: | Igor E. Shparlinski, Dragos Ghioca |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Algebra and Number Theory
Generator (category theory) 010102 general mathematics Prime number 0102 computer and information sciences 01 natural sciences Combinatorics Integer 010201 computation theory & mathematics Torsion (algebra) Order (group theory) Linear independence Drinfeld module 0101 mathematics Mathematics Additive group |
| Zdroj: | Journal of Number Theory. 233:112-125 |
| ISSN: | 0022-314X |
| Popis: | Let q be a power of the prime number p, let K = F q ( t ) , and let r ⩾ 2 be an integer. For points a , b ∈ K which are F q -linearly independent, we show that there exist positive constants N 0 and c 0 such that for each integer l ⩾ N 0 and for each generator τ of F q l / F q , we have that for all except N 0 values λ ∈ F q ‾ , the corresponding specializations a ( τ ) and b ( τ ) cannot have orders of degrees less than c 0 log log l as torsion points for the Drinfeld module Φ ( τ , λ ) : F q [ T ] ⟶ End F q ‾ ( G a ) (where G a is the additive group scheme), given by Φ T ( τ , λ ) ( x ) = τ x + λ x q + x q r . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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