Displaying similar documents to “A note on the zeros of exponential polynomials”

The Laguerre inequality and the distribution of zeros of entire functions

George Csordas, Alain Escassut (2005)

Annales mathématiques Blaise Pascal

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The Laguerre inequality and the distribution of zeros of real entire functions are investigated with the aid of certain infinite-order differential operators. The paper includes new proofs, problems, conjectures and many illustrative examples and counterexamples.

Some conjectures on the zeros of approximates to the Riemann ≡-function and incomplete gamma functions

James Haglund (2011)

Open Mathematics

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Riemann conjectured that all the zeros of the Riemann ≡-function are real, which is now known as the Riemann Hypothesis (RH). In this article we introduce the study of the zeros of the truncated sums ≡N(z) in Riemann’s uniformly convergent infinite series expansion of ≡(z) involving incomplete gamma functions. We conjecture that when the zeros of ≡N(z) in the first quadrant of the complex plane are listed by increasing real part, their imaginary parts are monotone nondecreasing. We show...