We derive general Novikov-Morse type inequalities in a Conley type framework for flows carrying cocycles, therefore generalizing our results in [FJ2] derived for integral cocycle. The condition of carrying a cocycle expresses the nontriviality of integrals of that cocycle on flow lines. Gradient-like flows are distinguished from general flows carrying a cocycle by boundedness conditions on thes...

In this study, a new identity involving conformable fractional integrals is given. Then, by using this identity, some new Hermite-Hadamard type inequalities for conformable fractional integrals have been developed.

A number of families of elliptic-type integrals have been studied recently due to their importance and potential for applications in some problems of radiation physics. The object of this work is to present a unified and generalized form of such elliptic-type integrals and to study its properties, including recurrence formulas and asymptotic expansion.

Some Hermite-Hadamard type inequalities for generalized k-fractional integrals (which are also named [Formula: see text]-Riemann-Liouville fractional integrals) are obtained for a fractional integral, and an important identity is established. Also, by using the obtained identity, we get a Hermite-Hadamard type inequality.

[C] A. Selberg, Harmonic analysis and discon-tinuous groups in weakly symmetric Rieman-nian spaces with applications to Dirichlet series ,

with fκ(s) as large as possible (resp. Fκ(s) as small as possible) given that the above inequality holds for all choices of A satisfying (1). Selberg [3] has shown (in a much more general context) that the functions fκ(s), Fκ(s) are continuous, monotone, and computable for s > 1, and that they tend to 1 exponentially as s goes to infinity. Let β = β(κ) be the infimum of s such that fκ(s) > 0. S...

We prove the Rankin-Selberg convolution of two cuspidal automorphic representations are automorphic whenever one of them arises from an irreducible representation of an abelian-by-nilpotent Galois extension, which extends the previous result of Arthur-Clozel. Moreover, if one of such representations is of dimension at most 3 and another representation arises from a nearly nilpotent extension or...

The analytic properties of the standard twist $F(s,\alpha)$, where $F(s)$ belongs to a wide class $L$-functions, are prime importance in describing structure Selberg class. In this paper we present deeper study such properties. particular, show that $F(s,\alpha)$ satisfies functional equation new type, somewhat resembling Hurwitz-Lerch zeta function. Moreover, detect finer polar characterizing ...

We study Riemann-type functional equations with respect to value-distribution theory and derive implications for their solutions. In particular, a fixed complex number $a\neq0$ function from the Selberg class $\mathcal{L}$, we prove Riemann-von Mangoldt formula of a-points $\Delta$-factor equation $\mathcal{L}$ an analog Landau's over these points. From last that ordinates $a$-points are unifor...