Dedekind sums and quadratic residue symbols of imaginary quadratic fields
نویسندگان
چکیده
منابع مشابه
Visualizing imaginary quadratic fields
Imaginary quadratic fields Q( √ −d), for integers d > 0, are perhaps the simplest number fields afterQ. They are equal parts helpful first example and misleading special case. LikeZ, the Gaussian integersZ[i] (the cased = 1) have unique factorization and a Euclidean algorithm. As d grows, however, these properties eventually fail, first the latter and then the former. The classical Euclidean al...
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is a modular form of weight n/2 on Γ0(N), where N is the level of Q, i.e. NQ−1 is integral and NQ−1 has even diagonal entries. This was proved by Schoeneberg [5] for even n and by Pfetzer [3] for odd n. Shimura [6] uses the Poisson summation formula to generalize their results for arbitrary n and he also computes the theta multiplier explicitly. Stark [8] gives a different proof by converting θ...
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Starting from the analytic class number formula involving its Lfunction, we first give an expression for the class number of an imaginary quadratic field which, in the case of large discriminants, provides us with a much more powerful numerical technique than that of counting the number of reduced definite positive binary quadratic forms, as has been used by Buell in order to compute his class ...
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We study the orbit of R under the Bianchi group PSL2(OK), where K is an imaginary quadratic field. The orbit, called a Schmidt arrangement SK , is a geometric realisation, as an intricate circle packing, of the arithmetic of K. This paper presents several examples of this phenomenon. First, we show that the curvatures of the circles are integer multiples of √ −∆ and describe the curvatures of t...
متن کاملClass numbers of imaginary quadratic fields
The classical class number problem of Gauss asks for a classification of all imaginary quadratic fields with a given class number N . The first complete results were for N = 1 by Heegner, Baker, and Stark. After the work of Goldfeld and Gross-Zagier, the task was a finite decision problem for any N . Indeed, after Oesterlé handled N = 3, in 1985 Serre wrote, “No doubt the same method will work ...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1991
ISSN: 0025-5645
DOI: 10.2969/jmsj/04330447