math.NT — Number Theory
Non-Archimedean Smale Mean Value and Dubinin–Sugawa Dual Mean Value Problems
Motivated by the Smale mean value and the Dubinin–Sugawa dual mean value theorems, we formulate non-Archimedean Smale mean value and Dubinin–Sugawa dual mean value problems. We show that if a universal constant satisfying the non-Archimedean Smale mean value problem exists, it must be greater than or equal to one and if a universal constant satisfying the non-Archimedean Dubinin–Sugawa dual mean value problem exists, it must be less than or equal to one. We also derive other bounds whenever roots of unity exist in a non-Archimedean field.
Primarily human-written textHuman understanding: all partsDubinin-Sugawa dual mean value theoremNon-Archimedean field.Smale mean value theorem