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  3. The Riemann Hypothesis
  • Cited by 4
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    • Publisher:
      Mathematical Association of America
      Publication date:
      26 May 2017
      01 March 2016
      ISBN:
      9780883859896
      9780883856505
      DOI:
      https://doi.org/10.5948/9780883859896
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      • Subjects:
      Mathematics, Number Theory
      Series:
      Anneli Lax New Mathematical Library
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    Subjects:
    Mathematics, Number Theory
    Series:
    Anneli Lax New Mathematical Library
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    Book description

    The Riemann hypothesis concerns the prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 ...Ubiquitous and fundamental in mathematics as they are, it is important and interesting to know as much as possible about these numbers. Simple questions would be: how are the prime numbers distributed among the positive integers? What is the number of prime numbers of 100 digits? Of 1,000 digits? These questions were the starting point of a groundbreaking paper by Bernhard Riemann written in 1859. As an aside in his article, Riemann formulated his now famous hypothesis that so far no one has come close to proving: All nontrivial zeroes of the zeta function lie on the critical line.

    Hidden behind this at first mysterious phrase lies a whole mathematical universe of prime numbers, infinite sequences, infinite products, and complex functions. The present book is a first exploration of this fascinating, unknown world. It originated from an online course for mathematically talented secondary school students organized by the authors of this book at the University of Amsterdam. Its aim was to bring the students into contact with challenging university level mathematics and show them what the Riemann Hypothesis is all about and why it is such an important problem in mathematics.

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