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  3. Duality in Analytic Number Theory
  • Cited by 19
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    • Publisher:
      Cambridge University Press
      Publication date:
      November 2011
      February 1997
      ISBN:
      9780511983405
      9780521560887
      9780521058087
      DOI:
      https://doi.org/10.1017/CBO9780511983405
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.64kg, 360 Pages
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.581kg, 360 Pages
      • Subjects:
      Mathematics (general), Mathematics, Number Theory, Discrete Mathematics Information Theory and Coding
      Series:
      Cambridge Tracts in Mathematics (122)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Number Theory, Discrete Mathematics Information Theory and Coding
    Series:
    Cambridge Tracts in Mathematics (122)
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    Book description

    In this stimulating book, aimed at researchers both established and budding, Peter Elliott demonstrates a method and a motivating philosophy that combine to cohere a large part of analytic number theory, including the hitherto nebulous study of arithmetic functions. Besides its application, the book also illustrates a way of thinking mathematically: historical background is woven into the narrative, variant proofs illustrate obstructions, false steps and the development of insight, in a manner reminiscent of Euler. It is shown how to formulate theorems as well as how to construct their proofs. Elementary notions from functional analysis, Fourier analysis, functional equations and stability in mechanics are controlled by a geometric view and synthesized to provide an arithmetical analogue of classical harmonic analysis that is powerful enough to establish arithmetic propositions until now beyond reach. Connections with other branches of analysis are illustrated by over 250 exercises, structured in chains about individual topics.

    Reviews

    ‘ … a fruitful atempt in finding a general method in Analytic Number Theory.’

    Source: Monatshefte für Mathematik

    ‘ … quite remarkable publication.’

    Source: European Mathematical Society

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