On the real roots of Bernoulli polynomials. (Sur les zéros réels des polynômes de Bernoulli.) (French) Zbl 0607.10006

The \(n\)th Bernoulli polynomial \(B_ n(x)\) is defined by \(B_ n(x+1)-B_ n(x)=nx^{n-1}\) and \(B_ n(0)=b_ n\), the \(n\)th Bernoulli number. In this very interesting note the author states a number of remarkable results on the real zeros of these polynomials. In many cases the number of real zeros can be determined exactly and approximate expressions for them can be given. Unfortunately the statements take too much space to quote here.
[For complex zeros see the following review.]
Reviewer: F. Beukers


11B83 Special sequences and polynomials
12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems)


Zbl 0607.10007