• Primes in Beatty sequence

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    • Keywords


      Beatty sequence; prime number; estimates on exponential sums.

    • Abstract


      For a polynomial $g(x)$ of deg $k \geq 2$ with integer coefficients and positive integer leading coefficient, we prove an upper bound for the least prime $p$ such that $g(p)$ is in non-homogeneous Beatty sequence $\{\lfloor \alpha n+ \beta\rfloor : n=1, 2, 3, \ldots\}$, where $\alpha , \beta\in R$ with $\alpha > 1$ is irrational and we prove an asymptotic formula for the number of primes $p$ such that $g(p) = \lfloor \alpha n+\beta\rfloor$. Next, we obtain an asymptotic formula for the number of primes $p$ of the form $p = \lfloor \alpha n+\beta \rfloor$ which also satisfies $p \equiv f (\mod d)$, where $f, d$ are integers with $1 \leq f$ < $d$ and $(f, d) = 1$.

    • Author Affiliations



      1. Institute of Mathematical Science, HBNI C.I.T Campus, Taramani, Chennai 600 113, India
    • Dates

  • Proceedings – Mathematical Sciences | News

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