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- W4287029056 abstract "We define a new class of functions, connected to the classical Laguerre-P'{o}lya class, which we call the shifted Laguerre-P'{o}lya 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 the Taylor coefficients, once shifted, being a degree $d$ multiplier sequence for every $d$, which is equivalent to shifted coefficients satisfying all of the higher T'{u}ran inequalities. This mirrors a classical result of P'{o}lya and Schur. We further show some order derivative of a function in this class satisfies each extended Laguerre inequality. Finally, we discuss some old and new conjectures about iterated inequalities for functions in this class." @default.
- W4287029056 created "2022-07-25" @default.
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- W4287029056 date "2021-08-03" @default.
- W4287029056 modified "2023-10-17" @default.
- W4287029056 title "On a new class of Laguerre-P'{o}lya type functions with applications in number theory" @default.
- W4287029056 hasPublicationYear "2021" @default.
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