On prime numbers of real quadratic fields in rectangles
نویسندگان
چکیده
منابع مشابه
Irregularity of Prime Numbers over Real Quadratic Fields
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...
متن کاملANote on the Divisibilityof Class Numbers of Real Quadratic Fields
Suppose g > 2 is an odd integer. For real number X > 2, define SgðXÞ the number of squarefree integers d4X with the class number of the real quadratic field Qð ffiffiffi d p Þ being divisible by g. By constructing the discriminants based on the work of Yamamoto, we prove that a lower bound SgðXÞ4X 1=g e holds for any fixed e > 0, which improves a result of Ram Murty. # 2002 Elsevier Science (USA)
متن کاملClass numbers of real cyclotomic fields of prime conductor
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 ...
متن کاملPrime 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 ...
متن کاملComputations of class numbers of real quadratic fields
In this paper an unconditional probabilistic algorithm to compute the class number of a real quadratic field Q( √ d) is presented, which computes the class number in expected time O(d1/5+ ). The algorithm is a random version of Shanks’ algorithm. One of the main steps in algorithms to compute the class number is the approximation of L(1, χ). Previous algorithms with the above running time O(d1/...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1936
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1936-1501853-1