Nagahama Institute of Bio-Science and Technology

SOME RESULTS ON NAIVE TRANSCENDENCE IN THE RING OF INTEGERS MODULO INFINITELY LARGE PRIMES

Abstract This paper presents various transcendence results in the ring of integers modulo infinitely large primes A $\mathcal {A}$ script upper A . In the ring A $\mathcal {A}$ script upper A , one can consider two notions of transcendence. One is based on the notion of finite al...

On the A $\mathcal {A}$ script upper A-transcendence of a Champernowne-type constant

Abstract Let p n $p_n$ p Subscript n denote the n th prime. We prove that, for every nonzero polynomial f ( x ) ∈ Z [ x ] $f(x)\in \mathbb {Z}[x]$ f left parenthesis x right parenthesis element of double struck upper Z left bracket x right bracket , there exist infinitely many po...