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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
| Autorius: | Kenneth S. Williams, J. Urbanowicz, |
| Serija: | Mathematics and Its Applications |
| Leidėjas: | Springer Netherlands |
| Išleidimo metai: | 2010 |
| Knygos puslapių skaičius: | 272 |
| ISBN-10: | 9048154901 |
| ISBN-13: | 9789048154906 |
| Formatas: | 235 x 155 x 15 mm. Knyga minkštu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „Congruences for L-Functions“
