Guloglu, Ahmet M.Luca, FlorianYalciner, Aynur2020-03-262020-03-2620180026-92551436-5081https://dx.doi.org/10.1007/s00605-018-1175-xhttps://hdl.handle.net/20.500.12395/36346Let 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.en10.1007/s00605-018-1175-xinfo:eu-repo/semantics/openAccessRational elliptic curvesChebotarev Density TheoremArithmetic functionsL-functionsEuler's totient functionElliptic pseudoprimesArticle1872247273Q2WOS:000443569700004Q2