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Mathematics and Its Applications

Congruences for L-Functions

Authors: Urbanowicz, J., Williams, Kenneth S.

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eBook 79,72 €
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  • ISBN 978-94-015-9542-1
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Hardcover 98,79 €
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Softcover 103,99 €
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About this book

In [Hardy and Williams, 1986] the authors exploited a very simple idea to obtain a linear congruence involving class numbers of imaginary quadratic fields modulo a certain power of 2. Their congruence provided a unified setting for many congruences proved previously by other authors using various means. The Hardy-Williams idea was as follows. Let d be the discriminant of a quadratic field. Suppose that d is odd and let d = PIP2· . . Pn be its unique decomposition into prime discriminants. Then, for any positive integer k coprime with d, the congruence holds trivially as each Legendre-Jacobi-Kronecker symbol (~) has the value + 1 or -1. Expanding this product gives ~ eld e:=l (mod4) where e runs through the positive and negative divisors of d and v (e) denotes the number of distinct prime factors of e. Summing this congruence for o < k < Idl/8, gcd(k, d) = 1, gives ~ (-It(e) ~ (~) =:O(mod2n). eld o

Table of contents (6 chapters)

  • Short Character Sums

    Urbanowicz, Jerzy (et al.)

    Pages 1-49

    Preview Buy Chapter 30,19 €
  • Class Number Congruences

    Urbanowicz, Jerzy (et al.)

    Pages 51-76

    Preview Buy Chapter 30,19 €
  • Congruences Between the Orders of K 2-Groups

    Urbanowicz, Jerzy (et al.)

    Pages 77-116

    Preview Buy Chapter 30,19 €
  • Congruences among the Values of 2-Adic L-Functions

    Urbanowicz, Jerzy (et al.)

    Pages 117-180

    Preview Buy Chapter 30,19 €
  • Applications of Zagier’s Formula (I)

    Urbanowicz, Jerzy (et al.)

    Pages 181-202

    Preview Buy Chapter 30,19 €

Buy this book

eBook 79,72 €
price for Spain (gross)
  • ISBN 978-94-015-9542-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 98,79 €
price for Spain (gross)
  • ISBN 978-0-7923-6379-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 103,99 €
price for Spain (gross)
  • ISBN 978-90-481-5490-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Congruences for L-Functions
Authors
Series Title
Mathematics and Its Applications
Series Volume
511
Copyright
2000
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-94-015-9542-1
DOI
10.1007/978-94-015-9542-1
Hardcover ISBN
978-0-7923-6379-8
Softcover ISBN
978-90-481-5490-6
Edition Number
1
Number of Pages
XII, 256
Topics