{ "item_title" : "Congruences for L-Functions", "item_author" : [" J. Urbanowicz", "Kenneth S. Williams "], "item_description" : "InHardy 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", "item_img_path" : "https://covers3.booksamillion.com/covers/bam/0/79/236/379/0792363795_b.jpg", "price_data" : { "retail_price" : "54.99", "online_price" : "54.99", "our_price" : "54.99", "club_price" : "54.99", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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