Title
Congruences for LFunctions (Mathematics and Its Applications, 511),New
Delivery time: 8-12 business days (International)
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 HardyWilliams 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 LegendreJacobiKronecker 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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This warranty strictly does not cover damages that arose from negligence, misuse, wear and tear, or not in accordance with product instructions (dropping the product, etc.).
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