Related papers: A remark on the Sibony function
In a previous paper we constructed all polynomial tau-functions of the 1-component KP hierarchy, namely, we showed that any such tau-function is obtained from a Schur polynomial $s_\lambda(t)$ by certain shifts of arguments. In the present…
In the paper, the authors establish integral representations of some functions related to the remainder of Burnside's formula for the gamma function and find the (logarithmically) complete monotonicity of these and related functions. These…
Renormdynamic equations of motion and their solutions are given. New equation for NBD distribution and Riemann zeta function invented. Explicit forms of the z-Scaling functions are constructed.
We prove an explicit upper bound of the function $S(t,\chi)$, defined by the argument of Dirichlet $L$-functions. An explicit upper bound of the function $S_1(t)$, defined by the integral of the argument of the Riemann zeta-function, have…
A formal description of a functional analysis approach to the Riemann zeta-functional equation that provides in principle an infinity of different proofs based on work by the author on the existence of dilation-invariant unitary operators…
In this article, we consider the set of points for the holding of the equality in a weighted version of Suita conjecture for higher derivatives, and give relations between the set and the integer valued points of a class of harmonic…
Bernoulli numbers are usually expressed in terms of their lower index numbers (recursive). This paper gives an explicit formula for Bernoulli numbers of even index. The formula contains a remarkable sequence of determinants.
We prove an explicit integral formula for computing the product of two shifted Riemann zeta functions everywhere in the complex plane. We show that this formula implies the existence of infinite families of exact exponential sum identities…
We introduce the good Hilbert functor and prove that it is algebraic. This functor generalizes various versions of the Hilbert moduli problem, such as the multigraded Hilbert scheme and the invariant Hilbert scheme. Moreover, we generalize…
The paper is discussing infinite divisibility in the setting of operator-valued boolean, free and, more general, c-free independences. Particularly, using Hilbert bimodules and non-commutative functions techniques, we obtain analogues of…
We derive asymptotic estimates at infinity for positive harmonic functions in a large class of non-smooth unbounded domains. These include domains whose sections, after rescaling, resemble a Lipschitz cylinder or a Lipschitz cone, e.g.,…
We show the hyperbolicity of the Feigenbaum fixed point using the inflexibility of the Feigenbaum tower, the Man\~e-Sad-Sullivan $\lambda$-Lemma and the existence of parabolic domains (petals) for semi-attractive fixed points.
We present an algorithm for computing a holonomic system for a definite integral of a holonomic function over a domain defined by polynomial inequalities. If the integrand satisfies a holonomic difference-differential system including…
We give a product expansion for the Drinfeld discriminant function in arbitrary rank $r$, which generalizes the formula obtained by Gekeler for the rank 2 Drinfeld discriminant function. This enables one to compute the Fourier expansion of…
A refinement of the Hardy inequality has been presented by use of superquadratic function.
We correct an inaccuracy in the original proof
We establish a general uniqueness theorem for subharmonic functions of several variables on a domain. A corollary from this uniqueness theorem for holomorphic functions is formulated in terms of the zero subset of holomorphic functions and…
A generalization of the classical Lipschitz summation formula is proposed. It involves new polylogarithmic rational functions constructed via the Fourier expansion of certain sequences of Bernoulli--type polynomials. Related families of…
We obtain pointwise estimates for solutions of semilinear parabolic equations with a potential on connected domains both of $\mathbb R^n$ and of general Riemannian manifolds.
In this article, we prove a Sobolev-like inequality for the Dirac operator on closed compact Riemannian spin manifolds with a nearly optimal Sobolev constant. As an application, we give a criterion for the existence of solutions to a…