Dilcher, Karl Zero-free regions for Bernoulli polynomials. (English) Zbl 0532.30005 C. R. Math. Acad. Sci., Soc. R. Can. 5, 241-246 (1983). The author continues his study of the complex zeros of the Bernoulli polynomials [begun in ibid. 5, 189-194 (1983; Zbl 0526.30007)]. He shows that the region \(x^ 2<c| y|,\quad c=2/33,\) contains no zero of \(B_ n(z+1/2)\) for \(n\geq 129.\) He also shows that the strip \(- .1577<x<1.1577\) contains no non-real zero of \(B_ n(z)\) for \(n\geq 1\), improving a result of R. Spira [Proc. Am. Math. Soc. 17, 1466-1467 (1966; Zbl 0154.319)]. In addition, he shows that the sections of the Maclaurin series for the sine and cosine have no zeros in the region \(x^ 2<c| y|\) with \(c=1/2\). Reviewer: D.W.Boyd Cited in 1 Document MSC: 30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) 33E99 Other special functions 30C10 Polynomials and rational functions of one complex variable Keywords:Bernoulli polynomial; sections of power series Citations:Zbl 0526.30007; Zbl 0154.319 PDFBibTeX XMLCite \textit{K. Dilcher}, C. R. Math. Acad. Sci., Soc. R. Can. 5, 241--246 (1983; Zbl 0532.30005)