共查询到20条相似文献,搜索用时 15 毫秒
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John Coates Takako Fukaya Kazuya Kato Ramdorai Sujatha Otmar Venjakob 《Publications Mathématiques de L'IHéS》2005,101(1):163-208
Let G be a compact p-adic Lie group, with no element of order p, and having a closed normal subgroup H such that G/H is isomorphic to Zp. We prove the existence of a canonical Ore set S* of non-zero divisors in the Iwasawa algebra Λ(G) of G, which seems to be particularly relevant for arithmetic applications. Using localization with respect to S*, we are able to define a characteristic element for every finitely generated Λ(G)-module M which has the property that the quotient of M by its p-primary submodule is finitely generated over the Iwasawa algebra of H. We discuss the evaluation of this characteristic element at Artin representations of G, and its relation to the G-Euler characteristics of the twists of M by such representations. Finally, we illustrate the arithmetic applications of these ideas by formulating a precise version of the main conjecture of Iwasawa theory for an elliptic curve E over Q, without complex multiplication, over the field F generated by the coordinates of all its p-power division points; here p is a prime at least 5 where E has good ordinary reduction, and G is the Galois group of F over Q. 相似文献
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Xin WAN 《数学学报(英文版)》2021,37(1):104-120
We prove an anticyclotomic Iwasawa main conjecture proposed by Perrin-Riou for Heegner points for semi-stable elliptic curves E over a quadratic imaginary field K satisfying a certain generalized Heegner hypothesis, at an ordinary prime p. It states that the square of the index of the anticyclotomic family of Heegner points in E equals the characteristic ideal of the torsion part of its Bloch–Kato Selmer group(see Theorem 1.3 for precise statement). As a byproduct we also prove the equality in the Greenberg–Iwasawa main conjecture for certain Rankin–Selberg product(Theorem 1.7) under some local conditions, and an improvement of Skinner's result on a converse of Gross–Zagier and Kolyvagin theorem(Corollary 1.11). 相似文献
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Generalizing and unifying prior results, we solve the subconvexity problem for the L-functions of GL 1 and GL 2 automorphic representations over a fixed number field, uniformly in all aspects. A novel feature of the present method is the softness of our arguments; this is largely due to a consistent use of canonically normalized period relations, such as those supplied by the work of Waldspurger and Ichino–Ikeda. 相似文献
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James W. Cogdell 《印度理论与应用数学杂志》2014,45(5):557-582
In classical analytic number theory there are several trace formulas or summation formulas for modular forms that involve integral transformations of test functions against classical Bessel functions. Two prominent such are the Kuznetsov trace formula and the Voronoi summation formula. With the paradigm shift from classical automorphic forms to automorphic representations, one is led to ask whether the Bessel functions that arise in the classical summation formulas have a representation theoretic interpretation. We introduce Bessel functions for representations of GL 2 over a finite field first to develop their formal properties and introduce the idea that the γ-factor that appears in local functional equations for L-functions should be the Mellin transform of a Bessel function. We then proceed to Bessel functions for representations of GL 2(?) and explain their occurrence in the Voronoi summation formula from this point of view. We briefly discuss Bessel functions for GL 2 over a p-adic field and the relation between γ-factors and Bessel functions in that context. We conclude with a brief discussion of Bessel functions for other groups and their application to the question of stability of γ-factors under highly ramified twists. 相似文献
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David E. Rohrlich 《Inventiones Mathematicae》1989,97(2):381-403
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Cristian D. Popescu 《Compositio Mathematica》1999,118(3):263-290
Based on results obtained in [15], we construct groups of special S-units for function fields of characteristic p>0, and show that they satisfy Gras-type Conjectures. We use these results in order to give a new proof of Chinburg's 3-Conjecture on the Galois module structure of the group of S-units, for cyclic extensions of prime degree of function fields. 相似文献
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Alexandre Nobs 《Mathematische Annalen》1977,229(2):113-133
Ohne ZusammenfassungUnterstütz durch den Sonderforschungsbereich 40, Bonn 相似文献
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《Differential Geometry and its Applications》2003,18(3):351-362
We study geometric properties of solvable metric Lie groups S of Iwasawa type; in particular harmonicity and the 2-stein condition. One restriction we obtain is that harmonic spaces of Iwasawa type have algebraic rank one, that is, the commutator subgroup of S has codimension one.We show that among Carnot solvmanifolds the only harmonic spaces are the Damek–Ricci spaces. Moreover, this rigidity result remains valid if harmonicity is replaced by the weaker 2-stein condition. As an application, we show that a harmonic Lie group of Iwasawa type with nonsingular 2-step nilpotent commutator subgroup is, up to scaling, a Damek–Ricci space. 相似文献
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Matthew. P. Young 《Mathematische Annalen》2013,356(3):1005-1028
For a fixed $SL(3,\mathbb Z )$ Maass form $\phi $ , we consider the family of $L$ -functions $L(\phi \times u_j, s)$ where $u_j$ runs over the family of Hecke-Maass cusp forms on $SL(2,\mathbb Z )$ . We obtain an estimate for the second moment of this family of $L$ -functions at the special points ${\frac{1}{2}}+ it_j$ consistent with the Lindelöf Hypothesis. We also obtain a similar upper bound on the sixth moment of the family of Hecke-Maass cusp forms at these special points; this is apparently the first occurrence of a Lindelöf-consistent estimate for a sixth power moment of a family of $GL(2) L$ -functions. 相似文献
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J. B. McLeod 《Studies in Applied Mathematics》1997,98(4):311-333
The integral equation:
φμ (s) = (1/3 π)∫π 0 ((sin φμ (t))/(μ −1 + ∫t 0 sin φμ (u) d u )) (log((sin½( s + t ))/ (sin½( s − t )))d t
was derived by Nekrasov to describe waves of permanent form on the surface of a nonviscous, irrotational, infinitely deep flow, the function φμ giving the angle that the wave surface makes with the horizontal. The wave of greatest height is the singular case μ=∞, and it is shown that there exists a solution φ∞ to the equation in this case and that it can be obtained as the limit (in a specified sense) as μ→∞ of solutions for finite μ. Stokes conjectured that φ∞ ( s )→⅙π as s ↓0, so that the wave is sharply crested in the limit case; and Krasovskii conjectured that sup s ∈[0,π] φμ ( s )≤⅙π for all finite μ. Stokes' conjecture was finally proved by Amick, Fraenkel, and Toland, and the present article shows Krasovskii's conjecture to be false for sufficiently large μ, the angle exceeding ⅙π in what is a boundary layer. 相似文献
φ
was derived by Nekrasov to describe waves of permanent form on the surface of a nonviscous, irrotational, infinitely deep flow, the function φ
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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
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Let be a cusp form on GL(2) over a number field F and let Ebe a quadratic extension of F. Denote by E the base change of to E and by a unitary character of AxE/ Ex. We use the relativetrace formula to give an explicit formula for L(1/2, E ) interms of period integrals of Gross–Prasad test vectors.We give an application of this formula to equidistribution ofgeodesics on a hyperbolic 3-fold. 相似文献
19.
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