Related papers: Regularly log-periodic functions and some applicat…

In this article, we study the local behaviour of the multiple zeta functions at integer points and write down a Laurent type expansion of the multiple zeta functions around these points. Such an expansion involves a convergent power series…

This article is devoted to derivation of the Laplace transforms of the derivatives with respect to parameters of certain special functions, namely, the Mittag-Leffler type, Wright and Le Roy type functions. These formulas show…

The present book gives a systematic overview of function theory and the theory of Stieltjes integral. In particular, we give a detailed account of the theory of functions of bounded variation and of the theory of regulated functions (=…

In this note, we describe a general procedure to prove functional equations involving quasi-periodic functions. We give novel proofs for fundamental identities of Weierstrass sigma and Jacobi theta functions. Our method is based on the…

We prove Siegel-Walfisz type theorems (over long and short intervals) for the Fourier coefficients of certain automorphic $L$-functions and Rankin-Selberg $L$-functions over number fields.

We consider multiply periodic functions, sometimes called Abelian functions, defined with respect to the period matrices associated with classes of algebraic curves. We realise them as generalisations of the Weierstras P-function using two…

We investigate the points of constancy in the piecewise constant solution profiles of the periodic linearized Korteweg--deVries equation with step function initial data at rational times. The solution formulas are given by certain Weyl…

We establish sharp upper bounds for shifted moments of quadratic Dirichlet $L$-function under the generalized Riemann hypothesis. Our result is then used to prove bounds for moments of quadratic Dirichlet character sums.

In this paper we present some applications of the Stieltjes constants including, for example, new derivations of Binet's formulae for the log gamma function and the evaluation of some integrals related to the Barnes multiple gamma…

A class of Stieltjes functions of finite type is introduced. These satisfy Widder's conditions on the successive derivatives up to some finite order, and are not necessarily smooth. We show that such functions have a unique integral…

In this paper some Tur\'an type inequalities for classical and generalized Mittag-Leffler functions are considered. The method is based on proving monotonicity for special ratio of sections for series of Mittag-Leffler functions. Some…

We show the smoothness of weakly Dirac-harmonic maps from a closed spin Riemann surface into stationary Lorentzian manifolds, and obtain a regularity theorem for a class of critical elliptic systems without anti-symmetry structures.

The paper surveys the basic properties of generalized Stieltjes functions including some new ones. We introduce the notion of the exact Stieltjes order and give a criterion of exactness, simple sufficient conditions and some prototypical…

The theory of slice regular functions of a quaternionic variable extends the notion of holomorphic function to the quaternionic setting. This theory, already rich of results, is sometimes surprisingly different from the theory of…

Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…

We introduce a new technique for proving the classical Stable Manifold theorem for hyperbolic fixed points. This method is much more geometrical than the standard approaches which rely on abstract fixed point theorems. It is based on the…

A nonstandard proof of a generalization of Karamata uniform convergence theorem for slowly varying functions is presented. Properties of a related operator $\mathcal{L}$ and its connection with slowly varying functions are discussed.

We prove the effectivity of the dynatomic cycles for morphisms of projective varieties. We then analyze the degrees of the dynatomic cycles and multiplicities of formal periodic points and apply these results to the existence of periodic…

In a recent article the authors obtained a formula which relates explicitly the tail of risk neutral returns with the wing behavior of the Black Scholes implied volatility smile. In situations where precise tail asymptotics are unknown but…

We investigate the structure of the set of $T$-periodic solutions to periodically perturbed coupled delay differential equations on differentiable manifolds. By using fixed point index and degree-theoretic methods we prove the existence of…