共查询到20条相似文献,搜索用时 15 毫秒
1.
Daniel Delbourgo 《Compositio Mathematica》1998,113(2):123-154
In this paper we examine the Iwasawa theory of modular elliptic curves E defined over Q without semi-stable reduction at p. By constructing p-adic L-functions at primes of additive reduction, we formulate a "Main Conjecture" linking this L-function with a certain Selmer group for E over the Zp-extension. Thus the leading term is expressible in terms of IIIE, E(Q)tors and a p-adic regulator term. 相似文献
2.
Let f(z) be a holomorphic cusp form of weight κ with respect to the full modular group SL2(Z). Let L(s, f) be the automorphic L-function associated with f(z) and χ be a Dirichlet character modulo q. In this paper, the authors prove that unconditionally for k =1/n with n ∈ N,and the result also holds for any real number 0 k 1 under the GRH for L(s, f ■χ).The authors also prove that under the GRH for L(s, f ■χ),for any real number k 0 and any large prime q. 相似文献
3.
Iwasawa theory of quadratic twists of <Emphasis Type="Italic">X</Emphasis><Subscript>0</Subscript>(49) 下载免费PDF全文
The field \(K = \mathbb{Q}\left( {\sqrt { - 7} } \right)\) is the only imaginary quadratic field with class number 1, in which the prime 2 splits, and we fix one of the primes p of K lying above 2. The modular elliptic curve X 0(49) has complex multiplication by the maximal order O of K, and we let E be the twist of X 0(49) by the quadratic extension \(KK(\sqrt M )/K\), where M is any square free element of O with M ≡ 1 mod 4 and (M,7) = 1. In the present note, we use surprisingly simple algebraic arguments to prove a sharp estimate for the rank of the Mordell-Weil group modulo torsion of E over the field F ∞ = K(E p∞), where E p∞ denotes the group of p∞-division points on E. Moreover, writing B for the twist of X 0(49) by \(K(\sqrt[4]{{ - 7}})/K\), our Iwasawa-theoretic arguments also show that the weak form of the conjecture of Birch and Swinnerton-Dyer implies the non-vanishing at s = 1 of the complex L-series of B over every finite layer of the unique Z2-extension of K unramified outside p. We hope to give a proof of this last non-vanishing assertion in a subsequent paper. 相似文献
4.
Root Numbers of Non-Abelian Twists of Elliptic Curves 总被引:2,自引:0,他引:2
We study the global root number of the complex L-function oftwists of elliptic curves over Q by real Artin representations.We obtain examples of elliptic curves over Q which, while nothaving any rational points of infinite order, conjecturallymust have points of infinite order over the fields for every cube-free m > 1. We describe analogousphenomena for elliptic curves over the fields , and in the towers and , where r 3 is prime.2000 Mathematics Subject Classification 11G40, 11G05. 相似文献
5.
Robert Pollack 《Journal of Number Theory》2005,110(1):164-177
Let E/Q be an elliptic curve and let p be an odd supersingular prime for E. In this article, we study the simplest case of Iwasawa theory for elliptic curves, namely when E(Q) is finite, ш(E/Q) has no p-torsion and the Tamagawa factors for E are all prime to p. Under these hypotheses, we prove that E(Qn) is finite and make precise statements about the size and structure of the p-power part of ш(E/Qn). Here Qn is the n-th step in the cyclotomic Zp-extension of Q. 相似文献
6.
7.
Let A be any one of the three elliptic curves over Q with conductor11. We show that A has MordellWeil rank zero over itsfield of 5-division points. In each case we also compute the5-primary part of the TateShafarevich group. Our calculationsmake use of the Galois equivariance of the CasselsTatepairing. 2000 Mathematics Subject Classification 11G05, 11Y40,11R23. 相似文献
8.
K. ONO 《Compositio Mathematica》1997,106(3):349-360
If E is an elliptic curve over
, then let E(D) denote theD-quadratic twist of E. It is conjectured that there are infinitely many primesp for which E(p) has rank 0, and that there are infinitely many primes
for which
has positive rank. For some special curvesE we show that there is a set S of primes p with density
for which if
is a squarefree integer where
, then E(D) has rank 0. In particular E(p) has rank 0 for every
. As an example let E1 denote the curve
.Then its associated set of primes S1 consists of the prime11 and the primes p for which the order of the reduction ofX0(11) modulo p is odd. To obtain the general result we show for primes
that the rational factor of L(E(p),1) is nonzero which implies thatE(p) has rank 0. These special values are related to surjective
Galois representations that are attached to modularforms. Another example of this result is given, and we conclude with someremarks regarding the existence of positive rank prime twists via polynomialidentities. 相似文献
10.
Matthew H. Baker 《Proceedings of the American Mathematical Society》1999,127(10):2851-2856
This paper gives a new proof of Kamienny's Criterion using the method of Coleman and Chabauty.
11.
In this note we show that, assuming the generalized Riemann hypothesis for quadratic imaginary fields, an irreducible algebraic curve in is modular if and only if it contains a CM point of sufficiently large height. This is an effective version of a theorem of Edixhoven. 相似文献
12.
13.
Larry Lehman. 《Mathematics of Computation》1997,66(218):833-839
We describe the explicit computation of linear combinations of ternary quadratic forms which are eigenvectors, with rational eigenvalues, under all Hecke operators. We use this process to construct, for each elliptic curve of rank zero and conductor for which or is squarefree, a weight 3/2 cusp form which is (potentially) a preimage of the weight two newform under the Shimura correspondence.
14.
Bas Edixhoven 《Compositio Mathematica》1998,114(3):307-320
We prove, assuming the generalized Riemann hypothesis for imaginary quadratic fields, the following special case of a conjecture of Oort, concerning Zarsiski closures of sets of CM points in Shimura varieties. Let X be an irreducible algebraic curve in C2, containing infinitely many points of which both coordinates are j-invariants of CM elliptic curves. Suppose that both projections from X to C are not constant. Then there is an integer m 1such that X is the image, under the usual map, of the modular curve Y20(m). The proof uses some number theory and some topological arguments. 相似文献
15.
Dirichlet L-函数倒数的2k次加权均值 总被引:3,自引:0,他引:3
本文主要目的是利用经典的Kloostermann和估计及其解析方法研究Dirich-let L-函数倒数的 2k次加权均值,得到了一个较为精确的渐近公式. 相似文献
16.
For two given ternary quadratic formsf(x, y, z) andg( x, y, z), letr(f, n) andr(g, n) be the numbers of representations of n represented byf( x, y, z) and g( x, y, z) respectively. In this paper we study the following problem: when will we haver(f, n) =r(g, n) orr( f, n)≠r(g, n). Our method is to use elliptic curves and the corresponding new forms. 相似文献
17.
Anna Iwaszkiewicz-Rudoszańska 《Monatshefte für Mathematik》1999,127(3):189-202
Under the Riemann Hypothesis for the classical Riemann zeta function, there exist infinitely many arithmetically non-isomorphic
arithmetical semigroups with the property that one of the associated L-functions vanishes at . Moreover, there are no restrictions in the distribution of prime divisors of a given norm except an obvious one concerning
the order of magnitude.
Received 22 December 1997 in revised form 12 May 1998 相似文献
18.
Suppose that E is an elliptic curve defined over a number field K, p is a rational prime, and K∞ is the maximal Zp-power extension of K. In previous work [B. Mazur, K. Rubin, Elliptic curves and class field theory, in: Ta Tsien Li (Ed.), Proceedings of the International Congress of Mathematicians, ICM 2002, vol. II, Higher Education Press, Beijing, 2002, pp. 185-195; B. Mazur, K. Rubin, Pairings in the arithmetic of elliptic curves, in: J. Cremona et al. (Eds.), Modular Curves and Abelian Varieties, Progress in Mathematics, vol. 224, 2004, pp. 151-163] we discussed the possibility that much of the arithmetic of E over K∞ (i.e., the Mordell-Weil groups and their p-adic height pairings, the Shafarevich-Tate groups and their Cassels pairings, over all finite extensions of K in K∞) can be described efficiently in terms of a single skew-Hermitian matrix with entries drawn from the Iwasawa algebra of K∞/K.In this paper, using work of Nekovár? [J. Nekovár?, Selmer complexes. Preprint available at 〈http://www.math.jussieu.fr/∼nekovar/pu/〉], we show that under not-too-stringent conditions such an “organizing” matrix does in fact exist. We also work out an assortment of numerical instances in which we can describe the organizing matrix explicitly. 相似文献
19.
H. Guo and T. Huang studied the four-weight spin models (X, W
1, W
2, W
3, W
4;D) with the property that the entries of the matrix W
2 (or equivalently W
4) consist of exactly two distinct values. They found that such spin models are always related to symmetric designs whose derived design with respect to any block is a quasi symmetric design. In this paper we show that such a symmetric design admits a four-weight spin model with exactly two values on W
2 if and only if it has some kind of duality between the set of points and the set of blocks. We also give some examples of parameters of symmetric designs which possibly admit four-weight spin models with exactly two values on W
2. 相似文献
20.
Anna Iwaszkiewicz-Rudoszańska 《Monatshefte für Mathematik》1999,83(5):189-202
Under the Riemann Hypothesis for the classical Riemann zeta function, there exist infinitely many arithmetically non-isomorphic arithmetical semigroups with the property that one of the associated L-functions vanishes at . Moreover, there are no restrictions in the distribution of prime divisors of a given norm except an obvious one concerning the order of magnitude. 相似文献