Wagner, Ian (2022). ON A NEW CLASS OF LAGUERRE-POLYA TYPE FUNCTIONS WITH APPLICATIONS IN NUMBER THEORY. Pac. J. Math., 320 (1). S. 177 - 194. BERKELEY: MATHEMATICAL SCIENCES PUBLISHERS. ISSN 1945-5844
Full text not available from this repository.Abstract
We define a new class of functions, connected to the classical Laguerre- Polya class, which we call the shifted Laguerre-Polya 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 d multiplier sequence for every d, which is equivalent to its shifted coefficients satisfying all of the higher Turan inequalities. This mirrors a classical result of Polya 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.
| Item Type: | Journal Article | ||||||||
| Creators: |
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| URN: | urn:nbn:de:hbz:38-659917 | ||||||||
| DOI: | 10.2140/pjm.2022.320.177 | ||||||||
| Journal or Publication Title: | Pac. J. Math. | ||||||||
| Volume: | 320 | ||||||||
| Number: | 1 | ||||||||
| Page Range: | S. 177 - 194 | ||||||||
| Date: | 2022 | ||||||||
| Publisher: | MATHEMATICAL SCIENCES PUBLISHERS | ||||||||
| Place of Publication: | BERKELEY | ||||||||
| ISSN: | 1945-5844 | ||||||||
| Language: | English | ||||||||
| Faculty: | Unspecified | ||||||||
| Divisions: | Unspecified | ||||||||
| Subjects: | no entry | ||||||||
| Uncontrolled Keywords: |
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| URI: | http://kups.ub.uni-koeln.de/id/eprint/65991 |
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