The sum of consecutive fractional parts
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The sum of the parts
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متن کاملEssay The sum of the parts
Essay The sum of the parts Graeme Mitchison Thirty years ago, Francis Crick, in his brilliant and combative little book Of Molecules and Men (Seattle: University of Washington; 1966), expounded what could be regarded as the biological reductionist's credo. The ultimate aim of a modern biologist, he said, should be to explain all biology in terms of physics and chemistry; in particular, it shoul...
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The sequence {B2}, {B4}, {B6}, ... is dense in the unit interval [0, 1], but it is not uniformly distributed [4]. Certain rational numbers appear with positive probability: 1/6 is most likely with probability 0.151..., 29/30 is next with probability 0.064... [5]. In fact, the limiting distribution F is piecewise linear with countably many jump discontinuities: F increases only when jumping (see...
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Using a recent improvement by Bettin and Chandee to a bound of Duke, Friedlander and Iwaniec (1997) on double exponential sums with Kloosterman fractions, we establish a uniformity of distribution result for the fractional parts of Dedekind sums s(m,n) with m and n running over rather general sets. Our result extends earlier work of Myerson (1988) and Vardi (1987). Using different techniques, w...
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ژورنال
عنوان ژورنال: Tsukuba Journal of Mathematics
سال: 1997
ISSN: 0387-4982
DOI: 10.21099/tkbjm/1496163166