Browsing by Author "Akbal,Y."

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    Cyclicity of Elliptic Curves Modulo Primes in Arithmetic Progressions
    (Cambridge University Press, 2022) Akbal,Y.; Güloǧlu,A.M.; Mathematics
    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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    Variations on a Theme of Mirsky
    (World Scientific, 2023) Akbal,Y.; Güloǧlu,A.M.; Mathematics
    Let k and r be non-zero integers with r ≥ 2. An integer is called r-free if it is not divisible by the rth power of a prime. A result of Mirsky states that there are infinitely many primes p such that p + k is r-free. In this paper, we study an additive Goldbach-type problem and prove two uniform distribution results using these primes. We also study certain properties of primes p such that p + a1,...,p + aℓ are simultaneously r-free, where a1,...,aℓ are non-zero integers and ℓ ≥ 1. © 2023 World Scientific Publishing Company.