Related papers: On Iwasawa $\lambda$-invariants for abelian number…

The Robinson-Schensted correspondence can be viewed as a map from permutations to partitions. In this work, we study the number of inversions of permutations corresponding to a fixed partition $\lambda$ under this map. Hohlweg characterized…

We formulate integral Iwasawa main conjectures for suitable twists of a newform $f$ that is non-ordinary at $p$, over the cyclotomic $\mathbb{Z}_p$-extension, the anticyclotomic $\mathbb{Z}_p$-extensions (in both the definite and the…

Analogues of Iwasawa invariants in the context of 3-dimensional topology have been studied by M.~Morishita and others. In this paper, following the dictionary of arithmetic topology, we formulate an analogue of Kida's formula on…

In 2010, Bezuglyi, Kwiatkowski, Medynets and Solomyak [Ergodic Theory Dynam. Systems 30 (2010), no.4, 973-1007] found a complete description of the set of probability ergodic tail invariant measures on the path space of a standard…

In this paper we establish a connection between the Gauss factorials and Iwasawa's cyclotomic $\lambda$-invariant for an imaginary quadratic field $K$. As a result, we will explain a corespondance between the 1-exceptional primes of…

Given $F$ a real abelian field, $p$ an odd prime and $\chi$ any Dirichlet character of $F$ we give a method for computing the $\chi$-index $\displaystyle (H^1(G_S,\mathbb{Z}_p(r))^\chi: C^F(r)^\chi)$ where the Tate twist $r$ is an odd…

Suppose $E$ is an elliptic curve over $\mathbb{Q}$ and $\chi$ is a Dirichlet character. We use statistical properties of modular symbols to estimate heuristically the probability that $L(E,\chi,1) = 0$. Via the Birch and Swinnerton-Dyer…

We study periodic points for endomorphisms $\sigma$ of abelian varieties $A$ over algebraically closed fields of positive characteristic $p$. We show that the dynamical zeta function $\zeta_\sigma$ of $\sigma$ is either rational or…

We study random partitions $\lambda=(\lambda_1,\lambda_2,...,\lambda_d)$ of $n$ whose length is not bigger than a fixed number $d$. Suppose a random partition $\lambda$ is distributed according to the Jack measure, which is a deformation of…

We progress with the investigation started in article \cite{Roman2022}, namely the analysis of the asymptotic behaviour of $Q_{\mathcal{P}}(x)$ for different sets $\mathcal{P}$, where $Q_{\mathcal{P}}(x)$ is the element count of the set…

Let $\varepsilon > 0$. We prove that there are constants $m_0=m_0(\varepsilon)$ and $\kappa=\kappa(\varepsilon) > 0$ for which the following holds: For every integer $m > m_0$ and every nontrivial Dirichlet character modulo $m$, there are…

The primary goal of this paper is to investigate the geometry of the $p$-adic eigencurve at a point $f$ corresponding to a weight one cuspidal theta series irregular at the prime number $p$. We show that $f$ belongs to exactly three or four…

Fix an odd prime $p$. Let $G$ be a compact $p$-adic Lie group containing a closed, normal, pro-$p$ subgroup $H$ which is abelian and such that $G/H$ is isomorphic to the additive group of $p$-adic integers $\mathbbZ_p$ . First we assume…

The reduction modulo $p$ of a family of lacunary integer polynomials, associated with the dynamical zeta function $\zeta_{\beta}(z)$ of the $\beta$-shift, for $\beta > 1$ close to one, is investigated. We briefly recall how this family is…

The Kida's formula in classical Iwasawa theory relates the Iwasawa $\lambda$-invariants of $p$-extensions of number fields. Analogue of this formula was subsequently established for the Iwasawa $\lambda$-invariants of Selmer groups under an…

We prove an analogue of Kida's formula for the Iwasawa invariants of the Mazur-Tate elements attached to elliptic curves over $\mathbb{Q}$. Let $p$ be an odd prime and let $L/K$ be a Galois extension of abelian number fields with $p$-power…

We study the singularity probability of n*n random matrices with i.i.d. entries from highly biased discrete distributions. We obtain sharp non-asymptotic bounds for this probability and derive estimates on the least singular values. Our…

Consider an irreducible, admissible representation $\pi$ of GL(2,$F$) whose restriction to GL(2,$F)^+$ breaks up as a sum of two irreducible representations $\pi_+ + \pi_-$. If $\pi=r_{\theta}$, the Weil representation of GL(2,$F$) attached…

Following the concentration of the measure theory formalism, we consider the transformation $\Phi(Z)$ of a random variable $Z$ having a general concentration function $\alpha$. If the transformation $\Phi$ is $\lambda$-Lipschitz with…

Zeros of the Riemann zeta function and its derivatives have been studied by many mathematicians. Among, the number of zeros and the distribution of the real part of non-real zeros of the derivatives of the Riemann zeta function have been…