Description
Book SynopsisThis book surveys the current state of the "small" sieve methods developed by Brun, Selberg and later workers. The book is suitable for university graduates making their first acquaintance with the subject, leading them towards the frontiers of modern research and unsolved problems in the subject area.
Trade ReviewFrom the reviews of the first edition:
"The author presents a self-contained account of the small sieve. … This well-written book will become my primary source for the small sieve … . I recommend it to everybody who is interested in the technically complicated theory on sieve methods." (R. Tijdeman, Nieuw Archief voor Wiskunde, Vol. 4 (3), 2003)
"The author’s choice of subjects provides a good background in the basic ideas of the sieve … . This text also supplies excellent background for some of the important unsolved problems of the subject. … In conclusion, the reviewer recommends this book strongly to students of sieve methods in the opening years of the twenty-first century. It will likely become one of the standard references on the subject." (Sidney W. Graham, Zentralblatt MATH, Vol. 1003 (03), 2003)
"The book being reviewed is an excellent survey on sieve methods. … The book is well written indeed, and most of the material can be described as self-contained. It can therefore be read by university graduates making their first acquaintance with the subject … ." (P. Shiu, The Mathematical Gazette, Vol. 86 (507), 2002)
Table of Contents1. The Structure of Sifting Arguments.- 2. Selberg’s Upper Bound Method.- 3. Combinatorial Methods.- 4. Rosser’s Sieve.- 5. The Sieve with Weights.- 6. The Remainder Term in the Linear Sieve.- 7. Lower Bound Sieves when ? > 1.- References.
