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001444927 001__ 1444927
001444927 003__ OCoLC
001444927 005__ 20230310003734.0
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001444927 019__ $$a1302120920$$a1302184307$$a1322446404
001444927 020__ $$a9783030731694$$q(electronic bk.)
001444927 020__ $$a3030731693$$q(electronic bk.)
001444927 020__ $$z9783030731687
001444927 020__ $$z3030731685
001444927 0247_ $$a10.1007/978-3-030-73169-4$$2doi
001444927 035__ $$aSP(OCoLC)1302105150
001444927 040__ $$aYDX$$beng$$erda$$epn$$cYDX$$dGW5XE$$dOCLCO$$dOCLCF$$dOCLCO$$dN$T$$dOCLCQ
001444927 049__ $$aISEA
001444927 050_4 $$aQA241$$b.R36 2022
001444927 08204 $$a512.7$$223
001444927 1001_ $$aRamaré, Olivier,$$eauthor.
001444927 24510 $$aExcursions in multiplicative number theory /$$cOlivier Ramaré ; with contributions by Pieter Moree and Alisa Sedunova.
001444927 264_1 $$aCham :$$bBirkhäuser,$$c[2022]
001444927 264_4 $$c©2022
001444927 300__ $$a1 online resource :$$billustrations (chiefly color).
001444927 336__ $$atext$$btxt$$2rdacontent
001444927 337__ $$acomputer$$bc$$2rdamedia
001444927 338__ $$aonline resource$$bcr$$2rdacarrier
001444927 4901_ $$aBirkhäuser advanced texts Basler Lehrbücher,$$x2296-4894
001444927 504__ $$aIncludes bibliographical references and indexes.
001444927 5050_ $$aApproach: Multiplicativity -- Arithmetic Convolution -- A Calculus on Arithmetical Functions -- Analytical Dirichlet Series -- Growth of Arithmetical Functions -- An "Algebraical" Multiplicative Function -- Möbius Inversions -- The Convolution Walk -- Handling a Smooth Factor -- The Convolution Method -- Euler Products and Euler Sums -- Some Practice -- The Hyperbola Principle -- The Levin-Faĭnleĭb Walk -- The Mertens Estimates -- The Levin-Fanleib Theorem -- Variations on a Theme of Chebyshev -- Primes in progressions -- A famous constant -- Euler Products with Primes in AP -- Chinese Remainder and Multiplicativity -- The Mellin Walk -- The Riemann zeta-function -- The Mellin Transform -- Proof Theorem Á -- Roughing up: Removing a Smoothening -- Proving the Prime Number Theorem -- Higher Ground: Applications / Extensions -- The Selberg Formula -- Rankin's Trick and Brun's Sieve -- Three Arithmetical Exponential Sums -- Convolution method / Möbius function -- The Large Sieve Inequality -- Montgomery's Sieve.
001444927 506__ $$aAccess limited to authorized users.
001444927 520__ $$aThis textbook offers a unique exploration of analytic number theory that is focused on explicit and realistic numerical bounds. By giving precise proofs in simplified settings, the author strategically builds practical tools and insights for exploring the behavior of arithmetical functions. An active learning style is encouraged across nearly three hundred exercises, making this an indispensable resource for both students and instructors. Designed to allow readers several different pathways to progress from basic notions to active areas of research, the book begins with a study of arithmetic functions and notions of arithmetical interest. From here, several guided "walks" invite readers to continue, offering explorations along three broad themes: the convolution method, the Levin-Faĭnleĭb theorem, and the Mellin transform. Having followed any one of the walks, readers will arrive at  "higher ground" where they will find opportunities for extensions and applications, such as the Selberg formula, Exponential sums with arithmetical coefficients, and the Large Sieve Inequality. Methodology is emphasized throughout, with frequent opportunities to explore numerically using computer algebra packages Pari/GP and Sage. Excursions in Multiplicative Number Theory is ideal for graduate students and upper-level undergraduate students who are familiar with the fundamentals of analytic number theory. It will also appeal to researchers in mathematics and engineering interested in experimental techniques in this active area.
001444927 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed March 9, 2022).
001444927 650_0 $$aNumber theory.
001444927 650_0 $$aMultiplication.
001444927 650_6 $$aThéorie des nombres.
001444927 650_6 $$aMultiplication (Arithmétique)
001444927 655_0 $$aElectronic books.
001444927 77608 $$iPrint version: $$z3030731685$$z9783030731687$$w(OCoLC)1241730564
001444927 830_0 $$aBirkhäuser advanced texts.$$x2296-4894
001444927 852__ $$bebk
001444927 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-73169-4$$zOnline Access$$91397441.1
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001444927 980__ $$aBIB
001444927 980__ $$aEBOOK
001444927 982__ $$aEbook
001444927 983__ $$aOnline
001444927 994__ $$a92$$bISE