|
This article is available for purchase or by subscription. See below.
Abstract
|
|
We define a new class of functions, connected to the classical Laguerre–Pólya class,
which we call the shifted Laguerre–Pólya class. Recent work of Griffin, Ono, Rolen, and
Zagier shows that the Riemann Xi function is in this class. We prove that a function
being in this class is equivalent to its Taylor coefficients, once shifted, being a degree
multiplier sequence
for every
,
which is equivalent to its shifted coefficients satisfying all of the higher Turán
inequalities. This mirrors a classical result of Pólya and Schur. For each function in
this class, we show some order derivative satisfies each extended Laguerre inequality.
Finally, we discuss some old and new conjectures about iterated inequalities for
functions in this class.
|
PDF Access Denied
We have not been able to recognize your IP address
3.129.211.87
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for
USD 40.00:
Keywords
Laguerre–Pólya class, Turán inequalities, Jensen
polynomials, partitions
|
Mathematical Subject Classification
Primary: 26C10, 26D20
|
Milestones
Received: 12 May 2022
Revised: 2 June 2022
Accepted: 25 June 2022
Published: 16 October 2022
|
|
