Related papers: Quadratic Euler-Kronecker constants in positive ch…

Let $K$ be an imaginary quadratic number field of class number one and $\mathcal{O}_K$ be its ring of integers. We show that, if the arithmetic functions $f, g:\mathcal{O}_K\rightarrow \mathbb{C}$ both have level of distribution $\vartheta$…

We consider moments of higher powers of quadratic Dirichlet character sums. In a restricted region, we give their asymptotic behavior by using de la Bret\`{e}che's multivariable Tauberian theorem. We also give the lower bound of the…

The spatial Fourier spectrum of the electron density distribution in a finite 1D system and the distribution function of electrons over single-particle states are studied in detail to show that there are two universal features in their…

We study properties of arithmetic sets coming from multiplicative number theory and obtain applications in the theory of uniform distribution and ergodic theory. Our main theorem is a generalization of K\'atai's orthogonality criterion.…

Measure rigidity is a branch of ergodic theory that has recently contributed to the solution of some fundamental problems in number theory and mathematical physics. Examples are proofs of quantitative versions of the Oppenheim conjecture,…

The article [HPS] established a monotonicity inequality for the Helmholtz equation and presented applications to shape detection and local uniqueness in inverse boundary problems. The monotonicity inequality states that if two scattering…

We investigate ergodic-theoretical quantities and large deviation properties of one-dimensional intermittent maps, that have not only an indifferent fixed point but also a singular structure such that the uniform measure is invariant under…

Motivated by various problems in physics and applied mathematics, we look for constraints and properties of real Fourier-positive functions, i.e. with positive Fourier transforms. Properties of the "Dirac comb" distribution and of its…

We give explicit computations of the $\Gamma$-Euler characteristic of several families of orbit space definable translation groupoids. These include the translation groupoids associated to finite-dimensional linear representations of the…

We consider Canonical Gibbsian ensembles of Euler point vortices on the 2-dimensional torus or in a bounded domain of R 2 . We prove that under the Central Limit scaling of vortices intensities, and provided that the system has zero global…

We formulate a model for the average behaviour of ray class groups of real quadratic fields with respect to a fixed rational modulus, locally at a finite set $S$ of odd primes. To that end, we introduce Arakelov ray class groups of a number…

We study the distribution functions of several classical error terms in analytic number theory, focusing on the remainder term in the Dirichlet divisor problem $\Delta(x)$. We first bound the discrepancy between the distribution function of…

Let $k=\mathbb{Q}(\sqrt{-3})$, and let $c\in \mathfrak{O}_k$ be a square free algebraic integer such that $c\equiv 1~({\rm mod}~{\langle9\rangle})$. Let $\zeta_{k(c^{1/3})}(s)$ be the Dedekind zeta function of the cubic field $k(c^{1/3})$…

The asymptotic expansion of digamma function is a starting point for the derivation of approximants for harmonic sums or Euler-Mascheroni constant. It is usual to derive such approximations as values of logarithmic function, which leads to…

Given a compact four dimensional manifold, we prove existence of conformal metrics with constant $Q$-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure.…

We prove joint universality theorems on the half plane of absolute convergence for general classes of Dirichlet series with an Euler-product, where in addition to vertical shifts we also allow scaling. This generalizes our recent joint…

Ramanujan studied a general class of Stirling constants that are the resummation of some natural divergent series. These constants include the classical Euler-Mascheroni, Stirling and Glaisher-Kinkelin constants. We find natural integral…

We consider the random lasing from a weakly scattering medium and demonstrate that the distribution of the threshold gain over the ensemble of statistically independent finite-size samples is universal. Universality stems from the facts…

We consider the evolution of an incompressible two-dimensional perfect fluid as the boundary of its domain is deformed in a prescribed fashion. The flow is taken to be initially steady, and the boundary deformation is assumed to be slow…

We develop Kummer theory for algebraic function fields in finitely many transcendental variables. We consider any finitely generated Kummer extension (possibly, over a cyclotomic extension) of an algebraic function field, and describe the…