Archivio Istituzionale della RicercaFor A ⊆ N, the question of when R(A) = {a/a0 : a, a0 ∈ A} is dense in the positive real numbers R+ has been examined by many authors over the years. In contrast, the p-adic setting is largely unexplored. We investigate conditions under which R(A) is dense in the p-adic numbers. Techniques from elementary, algebraic, and analytic number theory are employed in this endeavor. We also pose many open questions that should be of general interest.
p-adic quotient sets / Garcia, Stephan Ramon; Hong, Yu Xuan; Luca, Florian; Pinsker, Elena; Sanna, Carlo; Schechter, Evan; Starr, Adam. - In: ACTA ARITHMETICA. - ISSN 0065-1036. - STAMPA. - 179:2(2017), pp. 163-184. [10.4064/aa8579-4-2017]
p-adic quotient sets
Sanna, Carlo;
2017
Abstract
For A ⊆ N, the question of when R(A) = {a/a0 : a, a0 ∈ A} is dense in the positive real numbers R+ has been examined by many authors over the years. In contrast, the p-adic setting is largely unexplored. We investigate conditions under which R(A) is dense in the p-adic numbers. Techniques from elementary, algebraic, and analytic number theory are employed in this endeavor. We also pose many open questions that should be of general interest.
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https://hdl.handle.net/11583/2722657