Zeros of slice functions and polynomials over dual quaternions

Period polynomials, derivatives of L-functions, and zeros of polynomials

Period polynomials have long been fruitful tools for the study of values of L-functions in the context of major outstanding conjectures. In this paper, we survey some facets of this study from the perspective of Eichler cohomology. We discuss ways to incorporate non-cuspidal modular forms and values of derivatives of L-functions into the same framework. We further review investigations of the l...

Polynomials and Vandermonde Matrices over the Field of Quaternions

It is known that the space of real valued, continuous functions C(B) over a multidimensional compact domain B ⊂ R , k ≥ 2 does not admit Haar spaces, which means that interpolation problems in finite dimensional subspaces V of C(B) may not have a solutions in C(B). The corresponding standard short and elegant proof does not apply to complex valued functions over B ⊂ C. Nevertheless, in this sit...

Inequalities for products of zeros of polynomials and entire functions

Estimates for products of the zeros of polynomials and entire functions are derived. By these estimates, new upper bounds for the counting function are suggested. In appropriate situations we improve the Jensen inequality for the counting functions and the Mignotte inequality for products of the zeros of polynomials. Mathematics subject classification (2010): 26C10, 30C15, 30D20.

The Calculation of Zeros of Polynomials and Analytic Functions

On the Zeros of Polynomials and Related Analytic Functions

Let P(z) be a polynomial of degree n with real or complex coefficients, In this paper we obtain a ring shaped region containing all the zeros of P( z), Our results include, as special cases, several known extensions of Enestrom-Kakeya theorem on the zeros of a polynomiaL We shall also obtain zero free regions for certain class of analytic functions.