On differential independence of the Riemann zeta function and the Euler gamma function
Interpolating discrete multiplicity varieties for
A necessary and sufficient condition is obtained for a discrete multiplicity variety to be an interpolating variety for the space .
Interpolating varieties for weighted spaces of entire functions in C.
We prove in this paper that a given discrete variety V in C is an interpolating variety for a weight p if and only if V is a subset of the variety {ξ ∈ C: f(ξ) = f(ξ) = ... = f(ξ) = 0} of m functions f, ..., f in the weighted space the sum of whose directional derivatives in absolute value is not less than ε exp(-C(ζ)), ζ ∈ V for some constants ε, C > 0. The necessary and sufficient conditions will be also given in terms of the Jacobian matrix of f, ..., f. As a corollary, we solve an open...
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