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    Generator of PRN’s on the norm group
    (Одеський національний університет імені І. І. Мечникова, 2020) Fugelo, P.; Varbanets, Serhii P.; Фугело, П.; Варбанець, Сергій Павлович; Варбанец, Сергей Павлович
    Let 𝑝 be a prime number, 𝑑 ∈ N, (︁ −𝑑 𝑝 )︁ = −1, 𝑚 > 2, and let 𝐸𝑚 denotes the set of of residue classes modulo 𝑝𝑚 over the ring of Gaussian integers in imaginary quadratic field Q( √ −𝑑) with norms which are congruented with 1 modulo 𝑝𝑚. In present paper we establish the polynomial representations for real and imagimary parts of the powers of generating element 𝑢+𝑖𝑣 √ 𝑑 of the cyclic group 𝐸𝑚. These representations permit to deduce the “rooted bounds” for the exponential sum in Turan-Erd¨os-Koksma inequality. The new family of the sequences of pseudo-random numbers that passes the serial test on pseudorandomness was being buit. MSC: 11L07, 11T23, 11T71, 11K45.