{"product_id":"primedetecting-sieves-lms33-9780691124377","title":"PrimeDetecting Sieves LMS33","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eSeeks to describe the development in recent decades of sieve methods able to detect prime numbers. This work covers topics such as; primes in short intervals, the greatest prime factor of the sequence of shifted primes, Goldbach numbers in short intervals, the distribution of Gaussian primes, and the recent work of John Friedlander, and Iwaniec.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This book provides a very nice introduction to a very active and important area of research. Several chapters include discussion of the limitations of the given methods; this is an unusual feature but a very useful one to readers. There is also helpful discussion of historical developments of the given methods. This a valuable book, both for researchers and for advanced graduate students in analytic number theory.\"--S. W Graham, Mathematical Reviews \"[T]his book contains a valuable compendium of methods and results, and it will be of interest to aficionados of prime number theory.\"--Harold G. Diamond, SIAM Review \"The book is written in a very accessible style for a wide spectrum of readers... Besides mathematical ideas, the presentation also contains many important historical comments, which make the book useful for a general mathematical audience trying to orient themselves in the evolution of the main techniques applied in sieve methods.\"--EMS Newsletter\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface xi  Notation xiii  Chapter 1. Introduction 1  Chapter 2. The Vaughan Identity 25  Chapter 3. The Alternative Sieve 47  Chapter 4. The Rosser-Iwaniec Sieve 65  Chapter 5. Developing the Alternative Sieve 83  Chapter 6. An Upper-Bound Sieve 103  Chapter 7. Primes in Short Intervals 119  Chapter 8. The Brun-Titchmarsh Theorem on Average 157  Chapter 9. Primes in Almost All Intervals 189  Chapter 10. Combination with the Vector Sieve 201  Chapter 11. Generalizing to Algebraic Number Fields 231  Chapter 12. Variations on Gaussian Primes 265  Chapter 13. Primes of the Form x3 + 2y3 303  Chapter 14. Epilogue 335  Appendix 337  Bibliography 349  Index 361","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403740160343,"sku":"9780691124377","price":92.65,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/bookcurl.com\/products\/primedetecting-sieves-lms33-9780691124377","provider":"Book Curl","version":"1.0","type":"link"}