A generalization of arithmetic derivative to p-adic fields and number fields

HIGHLIGHTS

• What: The authors propose a new way to define the arithmetic derivative (resp. the arithmetic subderivative) DK (resp. From n i i (x)=0 for all n > j. (x) is a unit in OK, and thus DK,p (x))=0 the authors get DK,p νp (DK,p Now the authors show that if νp (x) ̸∈ {0, 1, 2,..., p - 1, +∞}, then the νp sequence of x is not i eventually +∞. The authors show that every anti-partial derivative x of DK,p (x0 ) is associated with a unique c ∈ C(x0 ). Next, the authors show that . . .
  

   

  

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