2017/10/26 by Divyum Sharma, Sharma, Divyum
Computer Science · Mathematics · #11A55 #11A63 #11J71 #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1710.09873
openalex publication_date 2017/10/26 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Let q be an integer \≥ 2 and let Sq(n) denote the sum of digits of\nn in base q. For\n n
alpha=[0;
overline1,m],
m
geq 2,\n let S\α(n) denote the sum of digits in the Ostrowski\n\α-representation of n. Let m1,m2\≥ 2 be integers with\n
gcd(q-1,m1)=
gcd(m,m2)=1. We prove that there exists \δ>0 such\nthat for all integers a1,a2,\n n amp;amp;|
0
leq nlt;N: Sq(n)
equiv a1
pmodm1,
S
alpha(n)
equiv\na2
pmodm2
|\n amp;=amp;
fracNm1m2+O(N1-
delta).\n The asymptotic relation implied by this equality was proved\nby Coquet, Rhin & Toffin and the equality was proved for the case \α=[ \n\1 ] by Spiegelhofer.\n