{"product_id":"congruences-for-l-functions-9780792363798","title":"Congruences for L-Functions","description":"\u003cp\u003e • Author(s): J. Urbanowicz\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Number Theory\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eIn [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\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Hardcover","offer_id":45283256467607,"sku":"9780792363798","price":3633.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780792363798.webp?v=1769304502","url":"https:\/\/atlanticbooks.com\/products\/congruences-for-l-functions-9780792363798","provider":"Atlantic Books","version":"1.0","type":"link"}