Related papers: Shifted convolution and the Titchmarsh divisor pro…
A q-analogue of four dimensional conformally invariant field theory based on the quantum algebra U_{q}(so(4,2)) is proposed. The two- and three-point correlation functions are calculated. The construction is elaborated in order to fit the…
The paper studies possible functional analogs of classical problems from convex geometry. In particular, we provide some bounds in the functional Shephard, Busemann-Petty, and Milman problems generalizing known bounds in this problems for…
In the theory of algebraic function fields and their applications to the information theory, the Riemann-Roch theorem plays a fundamental role. But its use, delicate in general, is efficient and practical for applications especially in the…
An important open problem in geometric complex analysis is to find algorithms for explicit determination of basic functionals intrinsically connected with conformal and quasiconformal maps, such as their Teichmuller and Grunsky norms,…
We establish bounds on a finite separable extension of function fields in terms of the relative class number, thus reducing the problem of classifying extensions with a fixed relative class number to a finite computation. We also solve the…
The article considers the Dirichlet problem for a high-order mixed-type equation that splits into factors, each of which is a Lavrentiev-Bitsadze equation with its own excellent coefficient. Sufficient conditions are found for the…
In classical potential theory, one can solve the Dirichlet problem on unbounded domains such as the upper half plane. These domains have two types of boundary points; the usual finite boundary points and another point at infinity. W. Woess…
We prove an equivariant Riemann-Roch formula for divisors on algebraic curves over perfect fields. By reduction to the known case of curves over algebraically closed fields, we first show a preliminary formula with coefficients in Q. We…
We prove a version of the Titchmarsh convolution theorem for distributions on the circle. We show that the "naive form" of the Titchmarsh theorem could be violated, but that such a violation is only possible for the convolution of…
Convolution powers of $1/x$ are transformed into functions $f_n$, which satisfy a simple recurrence relation. Solutions are characterized and analyzed.
The Dirichlet divisor problem is used as a model to give a conjecture concerning the conditional convergence of the Dirichlet series of an L-function.
We extend holomorphically polyharmonic functions on a real ball to a complex set being the union of rotated balls. We solve a Dirichlet type problem for complex polyharmonic functions with the boundary condition given on the union of…
While exploiting the generalized Parseval equality for the Mellin transform, we derive the reciprocal inverse operator in the weighted L_2-space related to the Hilbert transform on the nonnegative half-axis. Moreover, employing the…
Let $\tau$ denote the divisor function, and $f$ be any multiplicative function that satisfies some mild hypotheses. We establish the asymptotic formula or non-trivial upper bound for the shifted convolution sum $\sum_{n \leq…
The function $y=\Phi_\alpha(x)$, the solution of $y^\alpha e^y=x$ for $x$ and $y$ large enough, has a series expansion in terms of $\ln x$ and $\ln\ln x$, with coefficients given in terms of Stirling cycle numbers. It is shown that this…
We show that if $K$ is an arbitrary field and $G$ is a finite group then there exists a curve over $K$ with automorphism group $G$. We also give a positive solution to the weak inverse Galois problem for function fields over an arbitrary…
This paper analyzes the inverse problem of deautoconvolution in the multi-dimensional case with respect to solution uniqueness and ill-posedness. Deautoconvolution means here the reconstruction of a real-valued $L^2$-function with support…
The method of self-similar factor approximants is shown to be very convenient for solving different evolution equations and boundary-value problems typical of physical applications. The method is general and simple, being a straightforward…
By employing the $q$-difference operator, various classes of $q$-extensions of starlike functions have emerged from many different viewpoints and perspectives. Ruscheweyh's work unified these $q$-extensions with convolution operations.…
In \cite{NZ25}, the authors resolved the rational function analogue of the finiteness results for greatest common divisors of iterates of polynomials established in \cite{HT17}. These results may be viewed as dynamical generalizations of a…