Schatte, Peter On the asymptotic logarithmic distribution of the floating-point mantissas of sums. (English) Zbl 0607.60022 Math. Nachr. 127, 7-20 (1986). Let \(X_ 1,X_ 2,..\). be i.i.d. r.v.’s and \(S_ n=X_ 1+...+X_ n\). Then \(| S_ n| =Y_ n \exp K_ n\), where \(1\leq Y_ n<e\), \(K_ n\) an integer. The distribution function \(M_ n(x)\) of \(Y_ n\) is called the mantissa distribution of \(S_ n\). The \(M_ n(x)\) do not converge as \(n\to \infty\). But the \(H_{\infty}\)-method and the Riesz method of limitation enforce the convergence. The rate of convergence of these two methods is estimated in the article. The results are derived by first estimating Fourier coefficients and then employing the famous inequality of Erdős-Turán. Better estimates are recently obtained in a direct way by the author, the asymptotic behaviour of the mantissa distribution of sums. Elektron. Informationsverarbeitung Kybernetik 23, 7 ff. (1987). Cited in 1 ReviewCited in 3 Documents MSC: 60F05 Central limit and other weak theorems 68N99 Theory of software 60E15 Inequalities; stochastic orderings Keywords:mantissa distribution; Riesz method of limitation; inequality of Erdős- Turán × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Barlow, Computing 34 pp 349– (1985) [2] Benford, Proc. Amer. Philos. Soc. 78 pp 551– (1938) [3] Probabilistic number theory, vol. I. Springer, Berlin 1979 · doi:10.1007/978-1-4612-9989-9 [4] Flehinger, A. Amer. Math. Monthly 73 pp 1056– (1966) [5] The art of computer programming, vol. II: Seminumerical algorithms. Addison – Wesley, Reading (Mass.) 1969 · Zbl 0191.18001 [6] Sums of independent random variables. Akademie-Verlag, Berlin 1975 (Translation from the Russian) · doi:10.1007/978-3-642-65809-9 [7] Raimi, Amer. Math. Monthly 83 pp 521– (1976) [8] Schatte, Zeitschr. f. Angew. Math. und Mech. 53 pp 553– (1973) [9] Schatte, Wiss. Zeitschr. d. Univ. Rostock, Math.-Nat. Reihe 23 pp 783– (1974) [10] Schatte, Math. Nachr. 64 pp 63– (1974) [11] Schatte, Elektr. Inf. u. Kyber. 17 pp 293– (1981) [12] Schatte, Elektr. Inf. u. Kyber. 18 pp 523– (1982) [13] Schatte, Math. Nachr. 110 pp 243– (1983) [14] Schatte, Math. Nachr. 113 pp 237– (1983) [15] Schatte, Math. Nachr. 115 pp 275– (1984) [16] Schatte, Math. Nachr. 125 (1986) [17] und , Theorie der Limitierungsverfahren. Springer, Berlin 1970 · doi:10.1007/978-3-642-88470-2 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.