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On the log-concavity of a Jacobi theta function


Authors: Mark W. Coffey and George Csordas
Journal: Math. Comp. 82 (2013), 2265-2272
MSC (2010): Primary 26C10, 30D15; Secondary 30D10
DOI: https://doi.org/10.1090/S0025-5718-2013-02681-6
Published electronically: March 5, 2013
MathSciNet review: 3073199
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Abstract: A new proof of the log-concavity of the Jacobi theta function, appearing in the Fourier representation of the Riemann $ \Xi $ function, is presented. An open problem, involving the normalized moments of log-concave kernels, is investigated. In particular, several Turán-type inequalities are established.


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Additional Information

Mark W. Coffey
Affiliation: Department of Physics, Colorado School of Mines, Golden, Colorado 80401
Email: mcoffey@mines.edu

George Csordas
Affiliation: Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822
Email: george@math.hawaii.edu

DOI: https://doi.org/10.1090/S0025-5718-2013-02681-6
Keywords: Log-concavity, Jacobi theta function, Turán inequality, Riemann Xi-function
Received by editor(s): November 14, 2011
Received by editor(s) in revised form: January 23, 2012
Published electronically: March 5, 2013
Article copyright: © Copyright 2013 American Mathematical Society