The normality of digits in almost constant additive functions
نویسندگان
چکیده
منابع مشابه
Normality and the Digits of π
The question of whether (and why) the digits of well-known constants of mathematics are statistically random in some sense has long fascinated mathematicians. Indeed, one prime motivation in computing and analyzing digits of π is to explore the age-old question of whether and why these digits appear “random.” The first computation on ENIAC in 1949 of π to 2037 decimal places was proposed by Joh...
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0. Notations Throughout the paper we use the following notations: We write e(z) = e; C, R, Q, Z, N and N0, denote the set of complex numbers, real numbers, rational numbers, integers, positive integers, and positive integers including zero, respectively. Q(i) denotes the field of Gaussian numbers, and Z[i] the ring of Gaussian integers. We write tr(z) and N(z) for the trace and the norm of z ov...
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We consider the asymptotic behavior of b-additive functions f with respect to a base b of a canonical number system in the Gaussian number eld. In particular, we get a normal limit law for f(P (z)) where P (z) is a polynomial with integer coeecients. Our methods are exponential sums over the Gaussian number eld as well as certain results from the theory of uniform distribution. Throughout the p...
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ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2012
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-012-0453-2