Related papers: On the Jensen functional and superterzaticity
A recent result of Griffin, Ono, Rolen and Zagier on Jensen polynomials related with the Riemann zeta function is improved.
In this paper we show how the superquadratic functions can be used as a tool for researching other types of convex functions like $\phi $-convexity, strong-convexity and uniform convexity. We show how to use inequalities satisfied by…
We present new bounds for the Berezin number inequalities which improve on the existing bounds. We also obtain bounds for the Berezin norm of operators as well as the sum of two operators.
Lower and upper bounds for a given function are important in many mathematical and engineering contexts, where they often serve as a base for both analysis and application. In this short paper, we derive piecewise linear and quadratic…
We provide new upper bounds for sums of certain arithmetic functions in many variables at polynomial arguments and, exploiting recent progress on the mean-value of the Erd\H os-Hooley $\Delta$-function, we derive lower bounds for the…
We introduce new generalizations of the Gamma and the Beta functions. Their properties are investigated and known results are obtained as particular cases.
A generalization of a well-known relation between the Riemann zeta function $\zeta(s)$ and Bernoulli numbers $B_n$ is obtained. The formula is a new representation of the Riemann zeta function in terms of a nested series of Bernoulli…
We define zeta functions for the adjoint action of GL(n) on its Lie algebra and study their analytic properties. For n<4 we are able to fully analyse these functions, and recover the Shintani zeta function for the prehomogeneous vector…
In this paper, we derive new properties of the Mertens function and discuss a likely upper bound of the absolute value of the Mertens function $\sqrt{\log{x!}}>|M(x)|$ when $x>1$. Using this likely bound we show that we have a sufficient…
Given an nxn doubly stochastic matrix P satisfying an appropriate condition of linear algebraic-type, and a function f defined on a nonempty interval, we show that the validity of a convexity-type functional inequality for f in terms P…
The existence of the Herman ring of a function adds interest and complexity to the dynamics of the function. We present a detailed and understandable summary of the core discoveries and recent developments on the Herman ring of rational and…
In this paper we set up the theory of acid zeta function and ajoint acid zeta function, based on the theory, we point out a reason to doubt the truth of the Riemann hypothesis and also as a consequence, we give out some new RH equivalences.
We define the zeta function of a finite category. And we propose a conjecture which states the relationship between the Euler characteristic of finite categories and the zeta function of finite categories. This conjecture is verified when…
Under the Riemann hypothesis, we use the distribution of zeros of the zeta function to get a lower bound for the maximum of some derivative of Hardy's function.
Upper bounds are obtained for the $p$-capacity of compact sets in $\R^d$, with $d \ge 2$ and $1<p<d$. Upper and lower bounds are obtained for the product of $p$-capacity and powers of the $q$-torsional rigidity over the collection of all…
We investigate subclasses of generalized Bernstein functions related to complete Bernstein and Thorin-Bernstein functions. Representations in terms of incomplete beta and gamma as well as hypergeometric functions are presented. Several…
This paper deals with some simple results about spherical functions of type $\delta$, namely new integral formulas, new results about behavior at infinity and some facts about the related $C_\sigma$ functions.
We establish some monotonicity results and functional inequalities for modified Lommel functions of the first kind. In particular, we obtain new Tur\'{a}n type inequalities and bounds for ratios of modified Lommel functions of the first…
We present some new results in theory of classical theta-functions of Jacobi and sigma-functions of Weierstrass: ordinary differential equations (dynamical systems) and series expansions. The paper is basically organized as a stream of new…
The notion of the Jacob's ladders, reversely iterated integrals and the $\zeta$-factorization is used in this paper in order to obtain new results in study of the function $\arg\zf$. Namely, we obtain new formulae for non-local and…