TY - JOUR
T1 - On digit patterns in expansions of rational numbers with prime denominator
AU - Shparlinski, Igor E.
AU - Steiner, Wolfgang
PY - 2013/12
Y1 - 2013/12
N2 - We show that, for any fixed ε>0 and almost all primes p, the g-ary expansion of any fraction m/p with gcd(m, p)=1 contains almost all g-ary strings of length k < (17/72 - ε) logg p. This complements a result of J. Bourgain, S. V. Konyagin and I. E. Shparlinski, which asserts that, for almost all primes, all g-ary strings of length k < ( 41/504 - ε) logg p occur in the g-ary expansion of m/p.
AB - We show that, for any fixed ε>0 and almost all primes p, the g-ary expansion of any fraction m/p with gcd(m, p)=1 contains almost all g-ary strings of length k < (17/72 - ε) logg p. This complements a result of J. Bourgain, S. V. Konyagin and I. E. Shparlinski, which asserts that, for almost all primes, all g-ary strings of length k < ( 41/504 - ε) logg p occur in the g-ary expansion of m/p.
UR - http://www.scopus.com/inward/record.url?scp=84890663646&partnerID=8YFLogxK
U2 - 10.1093/qmath/has027
DO - 10.1093/qmath/has027
M3 - Article
AN - SCOPUS:84890663646
SN - 0033-5606
VL - 64
SP - 1231
EP - 1238
JO - Quarterly Journal of Mathematics
JF - Quarterly Journal of Mathematics
IS - 4
ER -