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    Arithmetic properties of coefficients of L-functions of elliptic curves
    (SPRINGER WIEN, 2018) Guloglu, Ahmet M.; Luca, Florian; Yalciner, Aynur
    Let n = 1 ann -s be the L-series of an elliptic curve E defined over the rationals without complex multiplication. In this paper, we present certain similarities between the arithmetic properties of the coefficients {an}8 n= 1 and Euler's totient function.(n). Furthermore, we prove that both the set of n such that the regular polygon with | an| sides is ruler-and-compass constructible, and the set of n such that n-an + 1 =.(n) have asymptotic density zero. Finally, we improve a bound of Luca and Shparlinski on the counting function of elliptic pseudoprimes.