Browsing by Subject "Chebotarev density theorem"

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    Cyclicity of elliptic curves modulo primes in arithmetic progressions
    (Cambridge University Press, 2021-05-03) Yıldırım, Akbal; Güloğlu, Ahmet M.
    We consider the reduction of an elliptic curve defined over the rational numbers modulo primes in a given arithmetic progression and investigate how often the subgroup of rational points of this reduced curve is cyclic.
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    Piatetski-shapir prime number theorem and chebotarev density theorem
    (2015-07) Akbal, Yıldırım
    Let K be a nite Galois extension of the eld Q of rational numbers. In this thesis, we derive an asymptotic formula for the number of the Piatetski-Shapiro primes not exceeding a given quantity for which the associated Frobenius class of automorphisms coincide with any given conjugacy class in the Galois group of K=Q. Applying this theorem to appropriate eld extensions, we conclude that there are in nitely many Piatetski-Shapiro primes lying in a given arithmetic progresion and furthermore there are in nitely many primes that can be expressed as a sum of a square and a xed positive integer multiple of another square.