共查询到20条相似文献,搜索用时 15 毫秒
1.
Dae San Kim 《Monatshefte für Mathematik》1998,126(1):55-71
For a nontrivial additive character and a multiplicative character of the finite field withq elements, the Gauss sums (trg) overgSp(2n,q) and (detg)(trg) overgGSp(2n, q) are considered. We show that it can be expressed as a polynomial inq with coefficients involving powers of Kloosterman sums for the first one and as that with coefficients involving sums of twisted powers of Kloosterman sums for the second one. As a result, we can determine certain generalized Kloosterman sums over nonsingular matrices and generalized Kloosterman sums over nonsingular alternating matrices, which were previously determined by J. H. Hodges only in the case that one of the two arguments is zero.Supported in part by Basic Science Research Institute program, Ministry of Education of Korea, BSRI 95-1414 and KOSEF Research Grant 95-K3-0101 (RCAA)Dedicated to my father, Chang Hong Kim 相似文献
2.
J.-M. Kim, S. Bae and I.-S. Lee showed that there exists an isomorphism between the p-primary part of the ideal class group and p-primary part of the unit group modulo cyclotomic unit group in Q+(ζpn) for all sufficiently large n under some conditions. In the present paper, we shall give an analogue of their result for modular units. 相似文献
3.
For thep-th cyclotomic fieldk, Iwasawa proved thatp does not divide the class number of its maximal real subfield if and only if the odd part of the group of local units coincides
with its subgroup generated by Jacobi sums related tok. We refine and give a quantitative version of this result for more general imaginary abelian fields. Our result is an analogy
of the famous result on “semi-local units modulo cyclotomic units”.
Partially supported by Grant-in-Aid for Scientific Research (C), Grant 09640054. 相似文献
4.
For the p-th cyclotomic field k, Iwasawa proved that p does not divide the class number of its maximal real subfield if and only if the odd part of the group of local units coincides
with its subgroup generated by Jacobi sums related to k. We refine and give a quantitative version of this result for more general imaginary abelian fields. Our result is an analogy
of the famous result on “semi-local units modulo cyclotomic units”.
Received: 2 May 1997 / Revised version: 11 November 1997 相似文献
5.
Yves Aubry 《Journal of Number Theory》2008,128(7):2053-2062
We show that, for any finite field Fq, there exist infinitely many real quadratic function fields over Fq such that the numerator of their zeta function is a separable polynomial. As pointed out by Anglès, this is a necessary condition for the existence, for any finite field Fq, of infinitely many real function fields over Fq with ideal class number one (the so-called Gauss conjecture for function fields). We also show conditionally the existence of infinitely many real quadratic function fields over Fq such that the numerator of their zeta function is an irreducible polynomial. 相似文献
6.
In this article, we investigate some conditions for a real cyclic extension K over Q to satisfy the property that every totally positive unit of K is a square. As an application, we give a partial answer to Taussky's conjecture. We then extend our result to real abelian extensions of certain type. 相似文献
7.
Pavel Kraemer 《Journal of Number Theory》2004,105(2):302-321
For a real abelian field with a non-cyclic Galois group of order l2, l being an odd prime, the index of the Sinnott group of circular units is computed. 相似文献
8.
Yutaka Konomi 《Journal of Number Theory》2011,131(6):1062-1069
We study the relation between the minus part of the p-class subgroup of a dihedral extension over an imaginary quadratic field and the special value of the Artin L-function at 0. 相似文献
9.
Hiroki Sumida-Takahashi 《Journal of Number Theory》2004,105(2):235-250
Let p be a prime number and k a finite extension of . It is conjectured that the Iwasawa invariants λp(k) and μp(k) vanish for all p and totally real number fields k. Some methods to verify the conjecture for each real abelian field k are known, in which cyclotomic units and a set of auxiliary prime numbers are used. We give an effective method, based on the previous one, to compute the exact value of the other Iwasawa invariant νp(k) by using Gauss sums and another set of auxiliary prime numbers. As numerical examples, we compute the Iwasawa invariants associated to in the range 1<f<200 and 5?p<10000. 相似文献
10.
We find an expression for a sum which can be viewed as a generalization of power moments of Kloosterman sums studied by Kloosterman
and Salié.
Received: 24 March 2006 相似文献
11.
Let k be an imaginary quadratic field in which the prime 2 splits. We consider the Iwasawa invariants of a certain non-cyclotomic
ℤ2-extension of k and give some sufficient conditions for the vanishing of λ- and μ-invariants. 相似文献
12.
We study a class of functional independences that the Iwasawa power series satisfy for both zero and non-zero characteristics. As results, we prove a generalization of Anglès and Ranieri [B. Anglès, G. Ranieri, On the linear independence of p-adic L-functions modulo p, Ann. Inst. Fourier (Grenoble) 60 (5) (2010) 1831–1855] and transcendence of the Iwasawa power series over the rational functions for non-zero characteristics. We also verify that the power series is not a solution of any non-trivial linear differential equation with the coefficients of rational functions over p-adic numbers. 相似文献
13.
Ming-Lun Hsieh 《Journal of Number Theory》2010,130(9):1914-1924
Because the analytic functional equation holds for Katz p-adic L-function for CM fields, the algebraic functional equation of the Selmer groups for CM fields is expected to hold. In this note we prove it following the specialization principle developed by T. Ochiai (2005) in [Och05]. 相似文献
14.
Sey Kim 《Journal of Number Theory》2006,121(1):7-29
Given any distinct prime numbers p,q, and r satisfying certain simple congruence conditions, we display a congruence relation between the fundamental units for the biquadratic field , modulo a certain prime ideal of OK. This congruence in particular implies the validity of the equivariant Tamagawa number conjecture formulated by Burns and Flach for the pair (h0(SpecK),Z[Gal(K/Q)]). 相似文献
15.
Humio Ichimura 《Journal of Number Theory》2008,128(4):858-864
Let p be a prime number. We say that a number field F satisfies the condition when for any cyclic extension N/F of degree p, the ring of p-integers of N has a normal integral basis over . It is known that F=Q satisfies for any p. It is also known that when p?19, any subfield F of Q(ζp) satisfies . In this paper, we prove that when p?23, an imaginary subfield F of Q(ζp) satisfies if and only if and p=43, 67 or 163 (under GRH). For a real subfield F of Q(ζp) with F≠Q, we give a corresponding but weaker assertion to the effect that it quite rarely satisfies . 相似文献
16.
Veronika Trnková 《Journal of Number Theory》2009,129(1):28-35
We compute the index of a certain extension of Sinnott's group of circular units in the group of all units of a bicyclic field. From this index we obtain some divisibility properties for class numbers of bicyclic fields. 相似文献
17.
David Vauclair 《Journal of Number Theory》2008,128(3):619-638
Following Kahn, and Assim and Movahhedi, we look for bounds for the order of the capitulation kernels of higher K-groups of S-integers into abelian S-ramified p-extensions. The basic strategy is to change twists inside some Galois-cohomology groups, which is done via the comparison of Tate Kernels of higher order. We investigate two ways: a global one, valid for twists close to 0 (in a certain sense), and a local one, valid for twists close to 1 in cyclic extensions. The global method produces lower bounds for abelian p-extensions which are S-ramified, but not Zp-embeddable. The local method is close to that of [J. Assim, A. Movahhedi, Bounds for étale capitulation kernels, K-Theory 33 (2004) 199-213], but is improved to take into consideration what happens when S consists of only the p-places. In contrast to the first one, one can expect this second method to produce nontrivial lower bounds in certain Zp-extensions. For example, we construct Zp-extensions in which the capitulation kernel is as big as we want (when letting the twist vary). We also include a complete solution to the problem of comparing Tate Kernels. 相似文献
18.
Stéphane Louboutin 《Journal of Number Theory》2010,130(4):956-960
Let ? be an algebraic unit such that rank of the unit group of the order Z[?] is equal to one. It is natural to ask whether ? is a fundamental unit of this order. To prove this result, we showed that it suffices to find explicit positive constants c1, c2 and c3 such that for any such ? it holds that c1c2|?|?d??c3|?|2c2, where d? denotes the absolute value of the discriminant of ?, i.e. of the discriminant of its minimal polynomial. We give a proof of this result, simpler than the original ones. 相似文献
19.
We consider Gauss sums for various finite classical groups, combine our previous results about explicit expressions for those sums with new ones obtained from our main formula based on Deligne-Lusztig theory and get some interesting identities, which are of combinatorial nature and involve various classical exponential sums. 相似文献
20.
Antonio Lei 《Journal of Number Theory》2010,130(10):2293-2307