Related papers: Global Units modulo Circular Units : descent witho…

For a weight two modular form and a good prime $p$, we construct a vector of Iwasawa functions $(L_p^\sharp,L_p^\flat)$. In the elliptic curve case, we use this vector to put the $p$-adic analogues of the conjectures of Birch and…

In this article, we provide a relation between the $\mu$-invariants of the dual plus and minus Selmer groups for supersingular elliptic curves when we ascend from the cyclotomic $\mathbb{Z}_p$-extension to a $\mathbb{Z}_p^2$-extension over…

We study this subject by first proving that the p-primary subgroup of the classical Selmer group for an elliptic curve with good, ordinary reduction at a prime p has a very simple and elegant description which involves just the Galois…

This paper is devoted to the asymptotic behavior of global solutions to the convection-diffusion equation in the Fujita-subcritical case. We improve the result by Zuazua (1993) and establish higher order asymptotic expansions with decay…

For an odd prime $p$ and a supersingular elliptic curve over a number field, this article introduces a fine signed residual Selmer group, under certain hypotheses on the base field. This group depends purely on the residual representation…

In this paper we develop a new method to study Iwasawa theory and Eisenstein families for unitary groups $\mathrm{U}(r,s)$ of general signature over a totally real field $F$. As a consequence we prove that for a motive corresponding to a…

In this paper we prove that the $p$-adic $L$-function that interpolates the Rankin-Selberg product of a general weight two modular form which is unramified and non-ordinary at $p$, and an ordinary CM form of higher weight contains the…

In \citenospec{MR1097615} several spectral sequences for (global and local) Iwasawa modules over (not necessarily commutative) Iwasawa algebras (mainly of $p$-adic Lie groups) over $\Z_p$ are established, which are very useful for…

Functional Renormalisation Group (FRG) equations are constructed for a simple Yukawa-model with discrete chiral symmetry, including also the effect of a nonzero composite fermion background beyond the conventional scalar condensate. The…

We extend to convenient finite quotients of a noetherian Lambda-module the classical result of K. Iwasawa giving the asymptotic expression of the l-part of the number of ideal class groups in Zl-extensions of number fields. Then, in the…

Given a prime $p\geq 5$, a conjecture of Greenberg predicts that the $\mu$-invariant of the $p$-primary Selmer group should vanish for most elliptic curves with good ordinary reduction at $p$. In support of this conjecture, I show that the…

It is known that there is a one-to-one correspondence between equivalence classes of primitive indefinite binary quadratic forms and primitive hyperbolic conjugacy classes of the modular group. Due to such a correspondence, Sarnak obtained…

Strong asymptotics of polynomials orthogonal on the unit circle with respect to a weight of the form $$ W(z) = w(z) \prod_{k=1}^m |z-a_k|^{2\beta_k}, \quad |z|=1, \quad |a_k|=1, \quad \beta_k>-1/2, \quad k=1, ..., m, $$ where $w(z)>0$ for…

We investigate a novel geometric Iwasawa theory for $\mathbf{Z}_p$-extensions of function fields over a perfect field $k$ of characteristic $p>0$ by replacing the usual study of $p$-torsion in class groups with the study of $p$-torsion…

Let F be a global function field of characteristic p with ring of integers A and let \Phi be a Hayes module on the Hilbert class field H(A) of F. We prove an Iwasawa Main Conjecture for the Z_p^\infty-extension F/F generated by the…

Let $p$ be a prime number. We investigate a refined version of the Iwasawa main conjectures for rational elliptic curves (and more general Galois representations) over anticyclotomic $\mathbb Z_p$-extensions of imaginary quadratic fields,…

The investigation of universality questions for local eigenvalue statistics continues to be a driving force in the theory of Random Matrices. For Matrix Models [53] the method of orthogonal polynomials can be used and the asymptotics of the…

We study the Iwasawa theory of $p$-primary Selmer groups of elliptic curves $E$ over a number field $K$. Assume that $E$ has additive reduction at the primes of $K$ above $p$. In this context, we prove that the Iwasawa invariants satisfy an…

Let $p$ be an odd prime. Let $f_1$ and $f_2$ be weight-two Hecke eigen-cuspforms with isomorphic residual Galois representations at $p$. Greenberg--Vatsal and Emerton--Pollack--Weston showed that if $p$ is a good ordinary prime for the two…

Let $K$ be a totally real number field of degree $r$. Let $K_{\infty}$ denote the cyclotomic $\mathbb{Z}_{2}$-extension of $K$ and let $L_{\infty}$ be a finite extension of $K_{\infty}$, abelian over $K$. The goal of this paper is to…