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A primer of analytic number theory : from Pythagoras to Riemann

By: Material type: TextTextLanguage: English Publication details: Cambridge Cambridge University Press 2003Description: xiii, 383p. illISBN:
  • 0521012538 (PB)
Subject(s):
Contents:
Ch. 1. Sums and Differences Ch. 2. Products and Divisibility Ch. 3. Order of Magnitude Ch. 4. Averages Interlude 1. Calculus Ch. 5. Primes Interlude 2. Series Ch. 6. Basel Problem Ch. 7. Euler's Product Interlude 3. Complex Numbers Ch. 8. The Riemann Zeta Function Ch. 9. Symmetry Ch. 10. Explicit Formula Interlude 4. Modular Arithmetic Ch. 11. Pell's Equation Ch. 12. Elliptic Curves Ch. 13. Analytic Theory of Algebraic Numbers.
Summary: This undergraduate introduction to analytic number theory develops analytic skills in the course of a study of ancient questions on polygonal numbers, perfect numbers, and amicable pairs. The question of how the primes are distributed among all integers is central in analytic number theory. This distribution is determined by the Riemann zeta function, and Riemann's work shows how it is connected to the zeros of his function and the significance of the Riemann Hypothesis.
Item type: BOOKS
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Home library Call number Materials specified Status Date due Barcode
IMSc Library 511.31 STO (Browse shelf(Opens below)) Available 50123

Includes index

Includes bibliography (p. 375-378) and references

Ch. 1. Sums and Differences Ch. 2. Products and Divisibility Ch. 3. Order of Magnitude Ch. 4. Averages Interlude 1. Calculus Ch. 5. Primes Interlude 2. Series Ch. 6. Basel Problem Ch. 7. Euler's Product Interlude 3. Complex Numbers Ch. 8. The Riemann Zeta Function Ch. 9. Symmetry Ch. 10. Explicit Formula Interlude 4. Modular Arithmetic Ch. 11. Pell's Equation Ch. 12. Elliptic Curves Ch. 13. Analytic Theory of Algebraic Numbers.

This undergraduate introduction to analytic number theory develops analytic skills in the course of a study of ancient questions on polygonal numbers, perfect numbers, and amicable pairs. The question of how the primes are distributed among all integers is central in analytic number theory. This distribution is determined by the Riemann zeta function, and Riemann's work shows how it is connected to the zeros of his function and the significance of the Riemann Hypothesis.

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The Institute of Mathematical Sciences, Chennai, India