An inequality for means with applications

DOI10.1007/S00013-007-2249-5zbMATH Open1140.26308arXiv1105.1372OpenAlexW3098618011MaRDI QIDQ2480693

Jan-Christoph Schlage-Puchta

Publication date: 3 April 2008

Published in: Archiv der Mathematik (Search for Journal in Brave)

Abstract: We show that an almost trivial inequality for the first and second mean of a random variable can be used to give non-trivial improvements on deep results. As applications we improve on results on lower bounds for the Riemann zeta-function on the critical line, the determinant of a skew-symmetric matrix with entries $pm1$, and on the maximal order of an irreducible character of the symmetric group.

Full work available at URL: https://arxiv.org/abs/1105.1372

zbMATH Keywords

Hadamard matricescharacter degreesmean valuefourth moment of zeta function

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Representations of finite symmetric groups (20C30) (zeta (s)) and (L(s, chi)) (11M06) Inequalities for sums, series and integrals (26D15)

Related Items (3)

A NEW MEAN WITH INEQUALITIES ⋮ On an approach in service of mean-inequalities ⋮ Interval-type theorems concerning means

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