共查询到20条相似文献,搜索用时 15 毫秒
1.
The fundamental result of the paper is the following theorem: suppose that the Riemann conjecture is valid for the Dedekind
ζ-functions of all fields
Then there exists a constant C>0 such that on the interval p≤x one can find at least Cx log−1 x prime numbers p for which h(5p2)=2. Here h(d) is the number of proper equivalence classes of primitive binary quadratic forms of discriminant d. In addition,
it is proved that
. For these sequence of discriminants of a special form with increasing square-free part, one has obtained a nontrivial estimate
from above for the number of classes.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR,
Vol. 160, pp. 72–81, 1987. 相似文献
2.
We prove that the class number of the real quadratic field
is divisible byn forany integern ≥ 2 andany odd integera ≥ 3. 相似文献
3.
Anitha Srinivasan. 《Mathematics of Computation》1998,67(223):1285-1308
In this paper an unconditional probabilistic algorithm to compute the class number of a real quadratic field is presented, which computes the class number in expected time . 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 . Previous algorithms with the above running time , obtain an approximation for by assuming an appropriate extension of the Riemann Hypothesis. Our algorithm finds an appoximation for without assuming the Riemann Hypothesis, by using a new technique that we call the `Random Summation Technique'. As a result, we are able to compute the regulator deterministically in expected time . However, our estimate of on the running time of our algorithm to compute the class number is not effective.
4.
Eduard Y. Lerner 《Functional Analysis and Other Mathematics》2010,3(1):75-83
In this paper we answer certain questions posed by V.I. Arnold, namely, we study periods of continued fractions for solutions
of quadratic equations in the form x
2+px=q with integer p and q, p
2+q
2≤R
2. We prove a weak variant of Arnold conjectures about the Gauss–Kuzmin statistics with R→∞. 相似文献
5.
Letp be an odd prime and
the finite field withp elements. In the present paper we shall investigate the number of points of certain quadratic hypersurfaces in the vector space
and derive explicit formulas for them. In addition, we shall show that the class number of the real quadratic field
(wherep1 (mod 4)) over the field of rational numbers can be expressed by means of these formulas. 相似文献
6.
The Ramanujan Journal - For a square-free integer t, Byeon (Proc. Am. Math. Soc. 132:3137–3140, 2004) proved the existence of infinitely many pairs of quadratic fields $$\mathbb... 相似文献
7.
E. P. Golubeva 《Journal of Mathematical Sciences》1996,79(5):1277-1292
For p prime, p≡3 (mod 4), we study the expansion of $\sqrt p$ into a continued fraction. In particular, we show that in the expansion $$\sqrt p = [n,\overline {l_1 ,...,l_L ,l,L_L ,...,l_1 ,2n} ]$$ l1, ... lL satisfy at least L/2 linear relations. We also obtain a new lower bound for the fundamental unit εp of the field ?( $\sqrt p$ ) for almost all p under consideration: εp > p3/log1+δp for all p≥x with O(x/log1+δx) possible exceptions (here δ>0 is an arbitrary constant), and an estimate for the mean value of the class number of ?( $\sqrt p$ ) with respect to averaging over εp: $$\sum\limits_{p \equiv 3 (\bmod 4), \varepsilon _p \leqslant x} {h(p) = O(x)}$$ . Bibliography: 11 titles. 相似文献
8.
9.
Periodica Mathematica Hungarica - We characterize p-rational real quadratic fields in terms of generalized Fibonacci numbers. We then use this characterization to give numerical evidence to a... 相似文献
10.
《Journal of Number Theory》1992,40(1):38-59
A function field version of a theorem of F. Hirzebruch relating continued fractions to class numbers of quadratic number fields is established. Our approach is based on Artin's thesis and Zagier's proof of Hirzebruch's theorem. Some of our results seem to be of independent interest, e.g. explicit formulas for Zeta functions of real quadratic function fields. 相似文献
11.
12.
E. P. Golubeva 《Journal of Mathematical Sciences》1999,95(3):2192-2197
We study the class number of an indefinite binary quadratic form of discriminant d based on the expansion of d into a continued fraction and single out sequences of d for which h(d) has a lower-bound extimate. Progress is made for the conjecture on the estimate of the quantity of prime discriminants d with fixed length of period of expansion of d. Bibliography: 15 titles.Dedicated to the 90th anniversary of G. M. Goluzin's birthTranslated fromZapiski Nauchnykh Seminarov POMI, Vol. 237, 1997, pp. 31–45. 相似文献
13.
The authors prove that the class number of the quadratic field Q(√?g) is divisible by 3 if g is a prime of the form 27n2 + 4. 相似文献
14.
We explain how one can dispense with the numerical computation of approximations to the transcendental integral functions involved when computing class numbers of quadratic number fields. We therefore end up with a simpler and faster method for computing class numbers of quadratic number fields. We also explain how to end up with a simpler and faster method for computing relative class numbers of imaginary abelian number fields.
15.
In this paper, we give a lower bound exp(2.2 × 10~8 ) for those discriminants of real quadratic fields Q(√ d) with d= N~2-4 and h(d)=1. 相似文献
16.
17.
Using the units appearing in Stark's conjectures on the values of -functions at , we give a complete algorithm for computing an explicit generator of the Hilbert class field of a real quadratic field.
18.
19.
20.
《Indagationes Mathematicae》2022,33(6):1189-1220
This paper investigates the quadratic irrationals that arise as periodic points of the Gauss type shift associated to the odd continued fraction expansion. It is shown that these numbers, which we call O-reduced, when ordered by the length of the associated closed primitive geodesic on some modular surface , are equidistributed with respect to the Lebesgue absolutely continuous invariant probability measure of the Odd Gauss shift. 相似文献