On the log-concavity of a Jacobi theta function
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- by Mark W. Coffey and George Csordas PDF
- Math. Comp. 82 (2013), 2265-2272 Request permission
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.References
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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
- Received by editor(s): November 14, 2011
- Received by editor(s) in revised form: January 23, 2012
- Published electronically: March 5, 2013
- © Copyright 2013 American Mathematical Society
- 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
- MathSciNet review: 3073199