A conjecture by Leon Ehrenpreis about zeroes of exponential polynomials

Alain Yger (1)

1 IMB - Institut de Mathématiques de Bordeaux

This survey paper reviews the (very few) facts actually known respect to a pending conjecture formulated by Leon Ehrenpreis in his 1970 book "Fourier analysis in several complex variables'' : distinct zeroes of an exponential polynomial in one variable with both algebraic coefficients and purely imaginary frequencies are well separated (in terms of the Paley-Wiener weight). We present here this conjecture and recall various methods that one could invoke to tackle it.

Mots clés: exponential-polynomials; spectral synthesis; ordinary differential equations

Domaines: Variables complexes [math.CV]; Théorie des nombres [math.NT]

Alain Yger. A conjecture by Leon Ehrenpreis about zeroes of exponential polynomials. 2011. ⟨hal-00618147v1⟩