Prime valued polynomials and class numbers of quadratic fields
نویسندگان
چکیده
منابع مشابه
Prime numbers and quadratic polynomials
Some nonconstant polynomials with a finite string of prime values are known; in this paper, some polynomials of this kind are described, starting from Euler’s example (1772) P(x) = x2+x+41: other quadratic polynomials with prime values were studied, and their properties were related to properties of quadratic fields; in this paper, some quadratic polynomials with prime values are described and ...
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Let K be an imaginary quadratic field with class number one and let p ⊂ OK be a degree one prime ideal of norm p not dividing 6dK . In this paper we generalize an algorithm of Schoof to compute the class numbers of ray class fields Kp heuristically. We achieve this by using elliptic units analytically constructed by Stark and the Galois action on them given by Shimura’s reciprocity law. We have...
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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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The concept of regular and irregular primes has played an important role in number theory at least since the time of Kummer. We extend this concept to the setting of arbitrary totally real number fields k0, using the values of the zeta function ζk0 at negative integers as our “higher Bernoulli numbers”. Once we have defined k0-regular primes and the index of k0-irregularity, we discuss how to c...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1990
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171290000011