On prime valued polynomials and class numbers of real 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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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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The class numbers h+l of the real cyclotomic fields Q(ζl + ζ −1 l ) are notoriously hard to compute. Indeed, the number h+l is not known for a single prime l ≥ 71. In this paper we present a table of the orders of certain subgroups of the class groups of the real cyclotomic fields Q(ζl + ζ −1 l ) for the primes l < 10, 000. It is quite likely that these subgroups are in fact equal to the class ...
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1988
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000001185