Mathematics of Computation

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Zeros of the Davenport-Heilbronn counterexample

Author(s): Eugenio P. Balanzario; Jorge Sánchez-Ortiz.
Journal: Math. Comp. 76 (2007), 2045-2049.
MSC (2000): Primary 11M26, 11M41
Posted: May 9, 2007
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Abstract: We compute zeros off the critical line of a Dirichlet series considered by H. Davenport and H. Heilbronn. This computation is accomplished by deforming a Dirichlet series with a set of known zeros into the Davenport-Heilbronn series.

References:

1.: Auslander, L.; Tolimieri, R., Is computing with the finite Fourier transform pure or applied mathematics? Bull. Amer. Math. Soc. (N.S.) 1 (1979), no. 6, 847-897. MR 546312 (81e:42020)
2.: Davenport, H.; Heilbronn, H., On the zeros of certain Dirichlet series I, II. J. London Math. Soc. 11 (1936), 181-185, 307-312.
3.: Spira, Robert., Some zeros of the Titchmarsh counterexample. Math. Comp. 63 (1994), no. 208, 747-748. MR 1254148 (95a:11081)


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