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020			_a9781470472030
040			_aNISER LIBRARY _beng _cNISER LIBRARY
041			_aEnglish
082			_a511 _bMUR-I
100	1		_aMurty, Maruti Ram.
245			_aIntroduction to the circle method
260			_aRhode Island : _bAmerican Mathematical Society, _c2023.
300			_axix, 257p.
490			_aStudent mathematical library, _vvolume 104 _x1520-9121 ;
504			_aIncludes bibliographical references and index.
520			_aThe circle method, pioneered by Ramanujan and Hardy in the early 20th century, has over the past 100 years become part of the standard tool chest of analytic number theory. Its scope of applications is ever-expanding, and the subject continues to see important breakthroughs. This book provides an introduction to the circle method that is accessible to undergraduate students with no background in number theory. The authors' goal is to show the students the elegance of the circle method and at the same time give a complete solution of the famous Waring problem as an illustration of the method. The first half of this book is a curated introduction to elementary number theory with an emphasis on topics needed for the second half. The second half showcases the two most “classic” applications of the circle method, to Waring's problem (following Hardy–Littlewood–Hua) and to Goldbach's conjectures (following Vinogradov, with improvements by Vaughan). This text is suitable for a one-semester undergraduate course or for independent study and will be a great entry point into this fascinating area of research.
521			_aUndergraduate and graduate students and researchers interested in the circle method, the Hardy-Littlewood method, Waring's problem, and Goldbach conjectures.
650		0	_aHardy-Littlewood method.
650		0	_aWaring's problem.
650		7	_aNumber theory -- Additive number theory; partitions -- Applications of the Hardy-Littlewood method.
650		7	_aNumber theory -- Additive number theory; partitions -- Goldbach-type theorems; other additive questions involving primes.
650		7	_aNumber theory -- Forms and linear algebraic groups -- Sums of squares and representations by other particular quadratic forms.
700	1		_aSinha, Kaneenika.
856			_3Table of Contents _uhttps://www.ams.org/bookstore/pspdf/stml-104-toc.pdf?_gl=1*1c6bplo*_ga*OTY4OTA1OTY3LjE3MTc5OTU1MTY.*_ga_26G4XFTR63*MTcxOTMwNTI2OC4zLjEuMTcxOTMxMTY5OC4wLjAuMA..
856			_3Reviews _uhttps://www.goodreads.com/book/show/195951234-an-introduction-to-the-circle-method?ref=nav_sb_ss_1_13#CommunityReviews
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