共查询到20条相似文献,搜索用时 0 毫秒
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David A. Clark 《manuscripta mathematica》1994,83(1):327-330
The classification of rings of algebraic integers which are Euclidean (not necessarily for the norm function) is a major unsolved
problem. Assuming the Generalized Riemann Hypothesis, Weinberger [7] showed in 1973 that for algebraic number fields containing
infinitely many units the ring of integersR is a Euclidean domain if and only if it is a principal ideal domain. Since there are principal ideal domains which are not
norm-Euclidean, there should exist examples of rings of algebraic integers which are Euclidean but not norm-Euclidean. In
this paper, we give the first example for quadratic fields, the ring of integers of
. 相似文献
3.
David Burns 《Journal of Number Theory》2004,107(2):282-286
We verify Gross's refined class number formula for abelian extensions of global function fields of prime exponent. 相似文献
4.
We study the arithmetic aspects of the finite group of extensions of abelian varieties defined over a number field. In particular, we establish relations with congruences between modular forms and special values of L-functions. 相似文献
5.
Masakazu Yamagishi 《Archiv der Mathematik》2007,88(4):304-315
We introduce a condition analogous to the Nielsen-Schreier formula, and investigate basic properties of pro-p-groups satisfying the condition.
Partly supported by the Grant-in Aid for Scientific Research (C), Japan Society for the Promotion of Science.
Received: 23 January 2006 相似文献
6.
The difference between the 3-rank of the ideal class group
of an imaginary quadratic field
and that of the associated real quadratic field
is equal to 0 or 1. In this note, we give an infinite family of
examples in each case.Received: 9 September 2002 相似文献
7.
A well known lemma attributed to Coburn states that a Toeplitz operator with non-trivial kernel acting on the Hardy space must have dense range. We show that the range of a non-zero Toeplitz operator with non-trivial kernel must contain all polynomials and state this in a precise form. 相似文献
8.
The number of Fq
-rational points of a plane non-singular algebraic curve
defined over a finite field Fq
is computed, provided that the generic point of
is not an inflexion and that
is Frobenius non-classical with respect to conics.
Received: 18 March 2003 相似文献
9.
We prove that the submodule in K-theory which gives the exact value
of the L-function by the Beilinson regulator map at non-critical values for Hecke characters of imaginary quadratic fields K with cl (K) = 1(p-local Tamagawa number conjecture) satisfies that the length of its coimage under the local Soulé regulator map is the p-adic valuation of certain special values of p-adic L-functions associated to the Hecke characters. This result yields immediately, up to Jannsens conjecture, an upper bound for
in terms of the valuation of these p-adic L-functions, where Vp denotes the p-adic realization of a Hecke motive.Received: 4 June 2003 相似文献
10.
O. Ramaré 《manuscripta mathematica》2007,124(1):59-75
We prove that every integer ≥ exp(524) is a sum of seven non negative cubes. 相似文献
11.
Kazuhiro Kurata 《Integral Equations and Operator Theory》2000,36(2):212-219
In this paper, we extend the result of Donig[Do] and show the finiteness of the lower spectrum of the uniformly elliptic operators–·(A(x))+q with singular potentialsq which belong to the Kato class. Even in the case of the Schrödinger operator–+q, our proof simplifies the one in [Do]. 相似文献
12.
Israel Feldman Naum Krupnik Ilya Spitkovsky 《Integral Equations and Operator Theory》1996,24(1):68-80
The norm of the above-mentioned operatorS is computed on the unions of parallel lines or concentric circles. The upper bound is found for its norm on the ellipse. In case of weighted spaces on the unit circle, the exact norm is found for some rational weights, and necessary and sufficient conditions on the weight are established, under which the essential norm ofS equals 1. 相似文献
13.
We study the asymptotic behaviour of solutions of the stochastic abstract Cauchy problem
$$ \left\{ {\begin{array}{*{20}l} {dU\left( t \right) = AU\left( t \right)dt + BdW_H \left( t \right),\quad t \geqslant 0,}
\hfill\ {U\left( 0 \right) = 0,} \hfill\ \end{array}} \right. $$ where A is the generator of a C0-semigroup on a Banach space E, WH is a cylindrical Brownian motion over a separable Hilbert space H, and
$$ B \in \user1{\mathscr L}\left( {H,E} \right) $$ is a bounded operator. Assuming the existence of a solution U, we prove that a unique invariant measure exists if the resolvent R(λ, A) is R-bounded in the right half-plane {Reλ > 0}, and that conversely the existence of an invariant measure implies the R-boundedness of R(λ, A)B in every half-plane properly contained in {Re λ > 0}. We study various abscissae related to the above problem and show, among
other things, that the abscissa of R-boundedness of the resolvent of A coincides with the abscissa corresponding to the existence of invariant measures for all γ -radonifying operators B provided the latter abscissa is finite. For Hilbert spaces E this result reduces to the Gearhart-Herbst-Prüss theorem.
Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday 相似文献
14.
《Journal of Number Theory》2003,101(1):32-47
Ostrowski established in 1919 that an absolutely irreducible integral polynomial remains absolutely irreducible modulo all sufficiently large prime numbers. We obtain a new lower bound for the size of such primes in terms of the number of integral points in the Newton polytope of the polynomial, significantly improving previous estimates for sparse polynomials. 相似文献
15.
The norms of them-th powers of the Volterra operatorV onL
2[0, 1] are computed form=1,...,10. These numbers suggest that the sequencem!V is bounded above and below, which is shown, and that this sequence converges to 1/2, which is conjectured. 相似文献
16.
(Quasi)-norms inC
p
andC
p, w
of weighted operators of the integration of (fractional) order are estimated. It is shown that, in most cases, the estimates obtained are sharp both in order and in function classes for the weight function involved. 相似文献
17.
In this paper we discuss Weyl matrix balls in the context of the matricial versions of the classical interpolation problems named after Carathéodory and Schur. Our particular focus will be on studying the monotonicity of suitably normalized semi-radii of the corresponding Weyl matrix balls. We, furthermore, devote a fair bit of attention to characterizing the case in which equality holds for particular matricial inequalities. Solving these problems will provide us with a new perspective on the role of the central functions for the classes of Carathéodory and Schur. 相似文献
18.
Shin Nakano 《Journal of Number Theory》2009,129(12):2943-2951
We give a family of quintic cyclic fields with even class number parametrized by rational points on an elliptic curve associated with Emma Lehmer's quintic polynomial. Further, we use the arithmetic of elliptic curves and the Chebotarev density theorem to show that there are infinitely many such fields. 相似文献
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We study the structure of the function field K of the quintic Fermat curve F(5) in the following way: Let K m be a g-maximal rational subfield of K. Then the field extension K/K m is obtained by the projection from F(5) to a line with a center p, ∈ F(5). By using this fact, we consider the field extension K/K m from several point of view. 相似文献