In this paper, we are concerned with orbital integrals on a class C of real reductive Lie groups with non-compact Iwasawa K-component. The class C contains all connected semisimple Lie groups with infinite center. We establish that any given orbital integral over general orbits with compactly supported continuous functions for a group G in C is convergent. Moreover, it is essentially the limit ...

We prove an anticyclotomic Iwasawa main conjecture proposed by Perrin-Riou for Heegner points semi-stable elliptic curves E over a quadratic imaginary field K satisfying certain generalized hypothesis, at ordinary prime p. It states that the square of index family in equals characteristic ideal torsion part its Bloch-Kato Selmer group (see Theorem 1.3 precise statement). As byproduct we also eq...

We use the notion of non-commutative Fitting invariants to give a reformulation of the equivariant Iwasawa main conjecture (EIMC) attached to an extension F/K of totally real elds with Galois group G, where K is a global number eld and G is a p-adic Lie group of dimension 1 for an odd prime p. We attach to each nite Galois CM-extension L/K with Galois group G a module SKu(L/K) over the center o...

Let K be an imaginary quadratic field where the prime p splits. Our goal in this article is to prove results towards Iwasawa main conjectures for p-nearly-ordinary families associated $$\mathrm {GL}_2\times \mathrm {Res}_{K/\mathbb {Q}}\mathrm {GL}_1$$ with a minimal set of assumptions. The technical input improvement on locally restricted Euler system machinery that allows treatment residually...

Poisson-Lie target space duality is a framework where duality transformations are properly defined. In this letter we investigate the dual pair of σ-models defined by the double SO(3,1) in the Iwasawa decomposition .

We derive an averaging property under the Iwasawa decomposition on a semisimple Lie group of noncompact type based on a limiting property of random walks in the Lie group.

We formulate and prove an analogue of the noncommutative Iwasawa main conjecture for `-adic Lie extensions of a separated scheme X of finite type over a finite field of characteristic prime to `.

A conceptual proof is given of the fact that the coefficients of the characteristic series of the U-operator acting on families of overconvegent modular forms lie in the Iwasawa algebra.

Finding a good metric over the input space plays a fundamental role in machine learning. Most existing techniques assume the Mahalanobis metric without incorporating the geometry of Pn, the space of n×n symmetric positive-definite (SPD) matrices, which leads to difficulties in the optimization procedure used to learn the metric. In this paper, we introduce a novel algorithm to learn the Mahalan...