Cauchy means of Dirichlet polynomials

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• 作者：Michel J.G. Weber ^{michel.weber@math.unistra.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Dirichlet polynomials ; Cauchy density ; Arctangent density ; Mean-value ; Mellin transform ; Spectral theory ; Homogeneous kernels ; Brownian motion
• 刊名：Journal of Approximation Theory
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：204
• 期：Complete
• 页码：61-79
• 全文大小：254 K

文摘

We study Cauchy means of Dirichlet polynomials These integrals were investigated when q=1,σ=1,s=1/2$q=1,\sigma =1,s=1/2$ by Wilf, using integral operator theory and Widom’s eigenvalue estimates. We show the optimality of some upper bounds obtained by Wilf. We also obtain new estimates for the case q≥1$q\ge 1$, σ≥0$\sigma \ge 0$ and s>0$s>0$. We complete Wilf’s approach by relating it with other approaches (having notably connection with Brownian motion), allowing simple proofs, and also prove new results.