SequencesTHIS volume is concerned with a substantial branch of number theory of which no connected account appears to exist; we describe the general nature of the constituent topics in the introduction. Although some excellent surveys dealing with limited aspects of the subject under con sideration have been published, the literature as a whole is far from easy to study. This is due in part to the extent of the literature; it is necessary to thread one's way through a maze of results, a complicated structure of inter-relationships, and many conflicting notations. In addition, however, not all the original papers are free from obscurities, and consequently some of these papers are difficult (a few even exceed ingly difficult) to master. We try to give a readable and coherent account of the subject, con taining a cross-section of the more interesting results. We felt that it would have been neither practicable nor desirable to attempt a compre hensive account; we treat each aspect of the subject from some special point of view, and select results accordingly. Needless to say, this approach entails the omission of many interesting and important results (quite apart from defects in the selection due to errors of judgement on our part). Those results selected for inclusion are, however, proved in complete detail and without the assumption of any prior knowledge on the part of the reader. |
Contents
STUDY OF DENSITY | 1 |
STUDY OF REPRESENTA | 76 |
STUDY OF REPRESENTA | 107 |
Copyright | |
5 other sections not shown
Other editions - View all
Common terms and phrases
a₁ additive applications asymptotic basis asymptotic density b₁ B₂-sequence Borel-Cantelli lemma Chapter completes the proof condition congruence classes connexion consists constant contains corresponding dB(A defined Definition degenerate modulo disjoint divisors Erdös estimate exists fact finite Furthermore Hence II(P implies inequality infinite integer sequences interval large sieve lim sup Linnik log log logarithmic density Math measurable space modulo g multiples natural numbers non-empty non-negative integers notation number of elements number theory numbers satisfying obtain order h pair prime factors prime number prime number theorem primitive sequence probability space probability theory proof of Theorem random variables real numbers remark Rényi residue classes result right-hand side rn(w Schnirelmann density Selberg set function sieve methods square-free subsets suffices to prove sufficiently Suppose Theorem 16 tion union whilst write zero Σ Σ