Titlebook: Number Theory; New York Seminar 198 David V. Chudnovsky,Gregory V. Chudnovsky,Melvyn B Conference proceedings 1991 Springer Science+Busines

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Classical Constants and Functions: Computations and Continued Fraction Expansions,ontinued fraction expansion of functions, and related fixed radix and continued fraction expansions of numbers. We try to classify all cases of closed form expressions of continued fraction expansions and present the corresponding identities. At the same time we want to understand what happens when no closed form expression exists.

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The Set of Multiples of a Short Interval, Thus if . (y, .] ∩Z. and .(.) is the set of multiples of ., then .(., y, .) is the counting function of .(.). To determine the asymptotic behaviour of this quantity with good precision is a difficult and interesting sieve problem with many applications in number theory — see in particular chap. 2 of [11].

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Introduction