Related papers: Zeros of some special entire functions

It is well known that real zeros of the Riemann zeta function are negative even integers. As for real zeros of the Hurwitz zeta function, T. Nakamura recently gave an existence condition in the intervals (0,1) and (-1,0). We generalize this…

We are concerned with the zeros of the Macdonald functions or the modified Bessel functions of the second kind with real index. By using the explicit expressions for the algebraic equations satisfied by the zeros, we describe the behavior…

The distribution of the zeros of the Euler double zeta-function $\zeta_2(s_1,s_2)$, in the case when $s_1=s_2$, is studied numerically. Some similarity to the distribution of the zeros of Hurwitz zeta-functions is observed.

Key words and phrases: q-Airy function (Ramanujan's entire function); q-Bessel function; Bessel function; Airy function; Riemann zeta function; Dirichlet L-series.

Zeros of Bessel functions $J_\alpha$ play an important role in physics. They are a motivation for studying zeros of exponential polynomials defined over $\overline{\mathbb{Q}}$, and more generally of $E$-functions. In this paper we…

Recently, Dixit et al. established a very elegant generalization of Hardy's Theorem concerning the infinitude of zeros that the Riemann zeta function possesses at its critical line. By introducing a general transformation formula for the…

We consider the variation of two fundamental types of zeta functions that arise in the study of both physical and analytical problems in geometric settings involving conical singularities. These are the Barnes zeta functions and the Bessel…

This paper deals with the study of the zeros of the big $q$-Bessel functions. In particular, we prove a new orthogonality relations for this functions similar to the one for the classical Bessel functions. Also we give some applications…

The paper proves a special case of a conjecture of Hellerstein, Shen and Williamson concerning non-real zeros of derivatives of real meromorphic functions.

We study entire functions whose zeros and one-points lie on distinct finite systems of rays. General restrictions on these rays are obtained. Non-trivial examples of entire functions with zeros and one-points on different rays are…

Special functions have been used widely in many problems of applied sciences. However, there are considerable numbers of problems in which exact solutions could not be achieved because of undefined sums or integrals involving special…

The z-zeros of the modified Bessel function of the third kind K_{nu}(z), also known as modified Hankel function or Macdonald function, are considered for arbitrary complex values of the order nu. Approximate expressions for the zeros,…

We generalize the work of Fei, Bhowmik and Halupczok, and Jia relating the Goldbach conjecture to real zeros of Dirichlet $L$-functions.

Algorithms for the computation of the real zeros of hypergeometric functions which are solutions of second order ODEs are described. The algorithms are based on global fixed point iterations which apply to families of functions satisfying…

Generalized integral formulas involving the generalized Bessel-Maitland function are considered and it expressed in terms of generalized Wright hypergeometric functions. By assuming appropriate values of the parameters in the main results,…

In this paper, we present results on the uniqueness of the real zeros of the Hurwitz zeta function in given intervals. The uniqueness in question, if the zeros exist, has already been proved for the intervals $(0,1)$ and $(-N, -N+1)$ for $N…

We establish the meromorphic continuation of certain multiple zeta functions of generalized Hurwitz type. From this meromorphic continuation, we obtain explicit formulas for their (derivative) values at nonpositive integers along a given…

Laguerre's theorem regarding the number of non-real zeros of a polynomial and its image under certain linear operators is generalized. This generalization is then used to (1) exhibit a number of previously undiscovered complex zero…

A number of results are proved concerning non-real zeros of derivatives of real meromorphic functions. In particular, the paper supersedes the previous arXiv submission "Non-real zeros of linear differential polynomials in real meromorphic…

We derive several identities for the Hurwitz and Riemann zeta functions, the Gamma function, and Dirichlet $L$-functions. They involve a sequence of polynomials $\alpha_k(s)$ whose study was initiated in an earlier paper. The expansions…