We investigate the monogamy relations related to the concurrence, the entanglement of formation, convex-roof extended negativity, Tsallis-q entanglement and Rényi-α entanglement, the polygamy relations related to the entanglement of formation, Tsallis-q entanglement and Rényi-α entanglement. Monogamy and polygamy inequalities are obtained for arbitrary multipartite qubit systems, which are proved to be tighter than the existing ones. Detailed examples are presented.

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Let r be a power of a prime number p, F r be the finite field of r elements, and F r [T] be the polynomial ring over F r . As an analogue to the Riemann zeta function over Z, Goss constructed the zeta function`F r [T] (s) over F r [T]. In order to study this zeta function, Thakur calculated the divided power series associated to the zeta measure + x on F r [T] v , where v is a finite place of F r (T ). This paper calculates the divided power series associated to the zeta measure on