On digit patterns in expansions of rational numbers with prime denominator
نویسندگان
چکیده
We show that, for any fixed ε > 0 and almost all primes p, the gary 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 that 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.
منابع مشابه
Computational Classification of Numbers and Algebraic Properties
In this paper, we propose a computational classification of finite characteristic numbers (Laurent series with coefficients in a finite field), and prove that some classes have good algebraic properties. This provides tools from the theories of computation, formal languages, and formal logic for finer study of transcendence and algebraic independence questions. Using them, we place some well-kn...
متن کاملSmall quotients in Euclidean algorithms
Numbers whose continued fraction expansion contains only small digits have been extensively studied. In the real case, the Hausdorff dimension σM of reals with digits in their continued fraction expansion bounded by M was considered, and estimates of σM for M → ∞ were provided by Hensley [12]. In the rational case, first studies by Cusick, Hensley and Vallée [4, 9, 19] considered the case of a ...
متن کاملTo appear in J. Théor. Nombres Bordeaux MINIMAL REDUNDANT DIGIT EXPANSIONS IN THE GAUSSIAN INTEGERS
We consider minimal redundant digit expansions in canonical number systems in the Gaussian integers. In contrast to the case of rational integers, where the knowledge of the two least significant digits in the “standard” expansion suffices to calculate the least significant digit in a minimal redundant expansion, such a property does not hold in the Gaussian numbers: We prove that there exist p...
متن کاملOptimal Rational Approximation Number Sets: Application to Nonlinear Dynamics in Particle Accelerators
We construct optimal multivariate vectors of rational approximation numbers with common denominator and whose coordinate decimal expansion string of digits coincides with the decimal expansion digital string of a given sequence of mutually irrational numbers as far as possible. We investigate several numerical examples and we present an application in Nuclear Physics related to the beam stabili...
متن کاملSubliminal Priming in Subtracting One-Digit Arabic Numbers
Background: Based on the studies which have investigated conscious and unconscious processes, simple arithmetic operations such as addition and multiplication can be automatically processed in the brain and affect subsequent responses. However, most studies have focused on addition and multiplication of one-digit numbers. In this research we used subliminal priming paradigm to assess automatic ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012