Related papers: On the comparison of the Dirichlet and Neumann cou…

We develop the convergence theory for a well-known method for the interpolation of functions on the real axis with rational functions. Precise new error estimates for the interpolant are de- rived using existing theory for trigonometric…

This paper surveys the theory of compactness of the d-bar-Neumann problem. It also contains several results which improve upon what was previously known.

We provide an introduction to Dirichlet forms on discrete spaces and study their global properties such as recurrence, stochastic completeness and regularity of the Neumann form. In this setting we compare the notion of a recurrent…

The Mahler measures of some n-variable polynomial families are given in terms of special values of the Riemann zeta function and a Dirichlet L-series, generalizing the results of \cite{L}. The technique introduced in this work also…

We present a simple way to derive the results of Diaconis and Fulman [arXiv:1102.5159] in terms of noncommutative symmetric functions.

In the paper, the author derives several "diagonal" recurrence relations, constructs some inequalities, finds monotonicity, and poses a conjecture related to Stirling numbers of the second kind.

This paper is concerned with the study of the fractional finite sums theory. We present the classes of functions for which it is possible to characterize the constant related to the derivative of fractional sums (denominated by essence of a…

In this paper weighted Dirichlet-type inequalities for the decreasing rearrangement in cylinders are proved. A weighted isoperimetric inequality is also obtained.

We prove the integrability of the discretization of the Neumann system recently proposed by V. Adler.

The purpose of this paper is to obtain some sufficient conditions to determine the relation between a meromorphic function and an L-function when certain differential polynomial generated by them sharing a one degree polynomial. The main…

This paper is an enhanced version of a more than decade-older paper with a similar title. Many formulae involving both finite and infinite sums of digamma and polygamma functions up to quadratic order, few of which appear in standard…

This paper treats the variation of sets. We attempt to formulate convergence and continuity of set-valued functions in a different way from the theories on sequences of sets and correspondence. In the final section, we also attempt to…

Linearly independent Dirichlet L-functions satisfying the same Riemann-type of functional equation have been supposed for long time to possess off critical line non trivial zeros. We are taking a closer look into this problem and into its…

We characterize those compact sets for which the Dirichlet problem has a solution within the class of continuous $m$-subharmonic functions defined on a compact set, and then within the class of $m$-harmonic functions.

The purpose of this paper is to give the explicit formulae of p-adic l-functions and sums of powers which are related to Euler numbers.

We prove general reflection positivity results for both scalar fields and Dirac fields on a Riemannian manifold, and comment on applications to quantum field theory. As another application, we prove the inequality $C_D \leq C_N$ between…

We prove an inequality featuring three well-known functions from analysis, namely the cotangent, the Euler-Riemann zeta function, and the digamma function. Aside from a simple proof of our result, we give a conjectured strengthening. We…

Integrating with respect to functions which are constant on intervals whose bounds are discontinuity points (of those functions) is frequent in many branches of Mathematics, specially in stochastic processes. For such functions and alike…

This thesis determines some of the implications of non-universal and emergent universal statistics on arithmetic correlations and fluctuations of arithmetic functions, in particular correlations amongst prime numbers and the variance of the…

The main purpose of this article is to study higher order moments of Kummer sums weighted by $L$-functions using estimates for character sums and analytic methods. The results of this article complement a conjecture of Zhang Wenpeng (2002).…