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Congruences for L-Functions by J. Urbanowicz

Congruences for L-Functions

by J. Urbanowicz
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Book cover type: Hardcover
  • ISBN13: 9780792363798
  • Binding: Hardcover
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 256
  • Original Price: EUR 49.99
  • Language: English
  • Edition: 2000
  • Item Weight: 563 grams
  • BISAC Subject(s): Number Theory, General, and Algebra / Abstract

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

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