2 research outputs found
Pairs of paths and critical points
Two sufficient conditions are presented, in terms of the values taken by a holomorphic function f(z) on a pair of smooth paths intersecting at a point z0 in its domain, implying that f′(z0)=0
On the ranges of discrete exponentials
Let a>1 be a fixed integer. We prove that there is no first-order formula ϕ(X) in one free variable X, written in the language of rings, such that for any prime p with gcd(a,p)=1 the set of all elements in the finite prime field Fp satisfying ϕ coincides with the range of the discrete exponential function t↦at(modp)