Related papers: Valuative analysis of planar plurisubharmonic func…
We study numerical invariants associated with the reduction of singularities of holomorphic foliation germs on $(\mathbb{C}^2, 0)$. Building on our previous work on generalized curve foliations, we extend explicit formulas for several…
Assuming the generalized Riemann hypothesis, we prove quantitative estimates for the number of simple zeros on the critical line for the L-functions attached to classical holomorphic newforms.
We consider Bernoulli distributions and their regularizations, which are measures on the $p$-adic integers $\mathbb{Z}_p$. It is well known that their Mellin transform can be used to define $p$-adic $L$-functions. We show that for $p>2$ one…
We study properties of relative types of plurisubharmonic functions with respect to maximal plurisubharmonic weights. It is shown that they give a general form for upper semicontinuous, tropically additive functionals on plurisubharmonic…
In this paper, I utilize a variant of the Selberg--Delange method to find quantitative estimates of the sums \[M_{k,\omega}(x,y)=\sum_{\substack{p_{1}(n)> y\\ n\leq x} } \mu(n) {\omega(n)-1\choose k-1},\] where $y$ can grow with $x$ but we…
In accordance with P. Vogel, a set of algebra structures in Chern-Simons theory can be made universal, independent of a particular family of simple Lie algebras. In particular, this means that various quantities in the adjoint…
The main goal of this work is to give new and precise generalizations to various classes of plurisubharmonic functions of the classical minimum modulus principle for holomorphic functions of one complex variable, in the spirit of the famous…
We study the problem of describing the set of real functionals on the quotient $\textrm{Sym}/(p_2-1)$ of the ring of symmetric functions that are nonnegative on the images of certain modified Hall-Littlewood symmetric functions. This…
The aim of the article is an extension of the Monodromy Conjecture of Denef and Loeser in dimension two, incorporating zeta functions with differential forms and targeting all monodromy eigenvalues, and also considering singular ambient…
We define a new rearrangement, called rearrangement by tamping, for non-negative measurable functions defined on R+. This rearrangement has many properties in common with the well-known Schwarz non-increasing rearrangement such as the…
Multi-valued functions are common in computable analysis (built upon the Type 2 Theory of Effectivity), and have made an appearance in complexity theory under the moniker search problems leading to complexity classes such as PPAD and PLS…
In this paper, we introduce a notion of singularity comparison for plurisubharmonic functions based on the Bedford--Taylor capacity. We establish comparison principles for the complex Monge--Amp\`ere operator on pluripolar sets in the…
This paper generalises the result of Jean-Pierre Demailly on his Ohsawa--Takegoshi-type $L^2$ extension theorem, which guarantees holomorphic extensions for some sections $f$ on analytic subspaces $Y$ defined by multiplier ideal sheaves of…
We give an estimate for the volume of an analytic variety (or more generally the mass of a positive closed current) close to a real submanifold $M$. Applications are given to the Hausdorff measure of the intersection of the variety with $M$…
Recently the authors have explored new concepts of plurisubharmonicity and pseudoconvexity, with much of the attendant analysis, in the context of calibrated manifolds. Here a much broader extension is made. This development covers a wide…
We consider the value distribution of logarithms of symmetric power L-functions associated with newforms of even weight and prime power level. In the symmetric square case, under certain plausible analytical conditions, we prove that…
Inspirations for this paper can be traced to Urbanik (1972) where convolution semigroups of multiple decomposable distributions were introduced. In particular, the classical gamma $\mathbb{G}_t$ and $\log \mathbb{G}_t$, $t>0$ variables are…
We consider the statistical distribution of zeros of random meromorphic functions whose poles are independent random variables. It is demonstrated that correlation functions of these zeros can be computed analytically and explicit…
We consider the pointwise approximation of a subharmonic function by the logarithm of the modulus of an entire function up to a bounded quantity. In the case of finite order an estimate from below of the planar Lebesgue measure of an…
Let $\mathcal{S}\subset \mathcal{L}^2 \subset \mathcal{S}^*$ be the Gel'fand triple over the Bernoulli space, where elements of $\mathcal{S}^*$ are called Bernoulli generalized functionals. In this paper, we define integrals of Bernoulli…