Related papers: On the comparison of the Dirichlet and Neumann cou…
This paper is a continuation of our recent paper with the same title, arXiv:0806.1596v1 [math.NT], where a number of integral equalities involving integrals of the logarithm of the Riemann zeta-function were introduced and it was shown that…
In the study of Dirichlet series with arithmetic significance there has appeared (through the study of known examples) certain expectations, namely (i) if a functional equation and Euler product exists, then it is likely that a type of…
Let $d$ be a real number, let $s$ be in a fixed compact set of the strip $1/2<\sigma<1$, and let $L(s, \chi)$ be the Dirichlet $L$-function. The hypothesis is that for any real number $d$ there exist 'many' real numbers $\tau$ such that the…
We prove new relations on zeta function at even arguments and Dirichlet $L$ function at odd. The key idea is to make use of the Taylor series and partial fraction decomposition of cotangent and secant functions as we discuss in calculus and…
We undertake a general study of multifractal phenomena for functions. We show that the existence of several kinds of multifractal functions can be easily deduced from an abstract statement, leading to new results. This general approach does…
We address the problem of evaluating an $L$-function when only a small number of its Dirichlet coefficients are known. We use the approximate functional equation in a new way and find that is possible to evaluate the $L$-function more…
We present a proof of the functional equation of the Riemann zeta-function or more precisely the Dirichlet eta-function, which proof seems to be new but follows almost immediately from Malmst\`en's paper ``De integralibus quibusdam…
The work studies some Difference equations, which are connected with Mejer's function.
A proof for the original Riemann hypothesis is proposed based on the infinite Hadamard product representation for the Riemann zeta function and later generalized to Dirichlet L-functions. The extension of the hypothesis to other functions…
We study the Dirichlet to Neumann operator of the $\overline{\partial}$-Neumann problem, and the relation between the $\overline{\partial}$-Neumann boundary conditions and the Dirichlet to Neumann operator.
The suggested approach is based on a known representation of Dirichlet $L$-functions via the incomplete gamma functions. Some properties of the Taylor coefficients of the lower incomplete gamma function at infinity seem to be new.…
R. M. Brown's theorem on mixed Dirichlet and Neumann boundary conditions is extended in two ways for the special case of polyhedral domains. A (1) more general partition of the boundary into Dirichlet and Neumann sets is used on (2)…
We correct a small gap found in the authors' paper 'On bounds for the effective differential Nullstellensatz' (J Algebra 449:1-21, 2016). This gap is due to an inequality that does not generally hold. However, under one additional…
The classical concept of $Q$-functions associated to symmetric and selfadjoint operators due to M.G. Krein and H. Langer is extended in such a way that the Dirichlet-to-Neumann map in the theory of elliptic differential equations can be…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
The Dirichlet problem and Dirichlet to Neumann map are analyzed for elliptic equations on a large collection of infinite quantum graphs. For a dense set of continuous functions on the graph boundary, the Dirichlet to Neumann map has values…
The manuscript reviews Dirichlet Series of important multiplicative arithmetic functions. The aim is to represent these as products and ratios of Riemann zeta-functions, or, if that concise format is not found, to provide the leading…
An analog of the Riemann hypothesis is proved in this paper. Some new integral equations for the functions $\pi(x)$ and $R(x)$ follows. A new effect that is shown is that these function - with essentially different behavior - are the…
We look at the values of two Dirichlet $L$-functions at the Riemann zeros (or a horizontal shift of them). Off the critical line we show that for a positive proportion of these points the pairs of values of the two $L$-functions are…
An approximate formula for complex Riemann Xi function, previously developed, is used to refine Backlund's estimate of the number of zeros till a chosen imaginary coordinate