The Jensen–Pólya program for various L-functions
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Ian Wagner
Abstract
Pólya proved in 1927 that the Riemann hypothesis is equivalent to the hyperbolicity of all of the Jensen polynomials of degree d and shift n for the Riemann Xi-function. Recently, Griffin, Ono, Rolen, and Zagier [M. Griffin, K. Ono, L. Rolen and D. Zagier,
Jensen polynomials for the Riemann zeta function and other sequences,
Proc. Natl. Acad. Sci. USA 116 2019, 23, 11103–11110] proved that for each degree
Acknowledgements
The author would like to thank Larry Rolen, Michael Griffin, and Ken Ono for helpful discussions related to this work and the referee for many suggestions which improved the clarity of this paper.
References
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Operational rules and generalized special polynomials
- Linearity of some low-complexity mapping class groups
- Ultramatricial algebras over commutative chain semirings and application to MV-algebras
- On a group analogue of the Heyde theorem
- Explicit presentation of an Iwasawa algebra: The case of pro-p Iwahori subgroup of SLn(ℤp)
- Generalized Riesz potentials of functions in Morrey spaces L(1,ϕ;κ)(G) over non-doubling measure spaces
- On rough singular integrals along real-analytic submanifolds
- Dimension-free estimates for the vector-valued variational operators
- Upper bound of multiplicity in prime characteristic
- Asymptotic behaviour for elliptic operators with second-order discontinuous coefficients
- Irreducible and permutative representations of ultragraph Leavitt path algebras
- Twisted tensor products of φ-coordinated modules for nonlocal vertex algebras
- Explicit decomposition theorem for special Schubert varieties
- On the Hirzebruch–Kobayashi–Ono proportionality principle and the non-existence of compact solvable Clifford–Klein forms of certain homogeneous spaces
- The Lie group of vertical bisections of a regular Lie groupoid
- Chain conditions for graph C*-algebras
- Congruences in Hermitian Jacobi and Hermitian modular forms
- The Jensen–Pólya program for various L-functions
Artikel in diesem Heft
- Frontmatter
- Operational rules and generalized special polynomials
- Linearity of some low-complexity mapping class groups
- Ultramatricial algebras over commutative chain semirings and application to MV-algebras
- On a group analogue of the Heyde theorem
- Explicit presentation of an Iwasawa algebra: The case of pro-p Iwahori subgroup of SLn(ℤp)
- Generalized Riesz potentials of functions in Morrey spaces L(1,ϕ;κ)(G) over non-doubling measure spaces
- On rough singular integrals along real-analytic submanifolds
- Dimension-free estimates for the vector-valued variational operators
- Upper bound of multiplicity in prime characteristic
- Asymptotic behaviour for elliptic operators with second-order discontinuous coefficients
- Irreducible and permutative representations of ultragraph Leavitt path algebras
- Twisted tensor products of φ-coordinated modules for nonlocal vertex algebras
- Explicit decomposition theorem for special Schubert varieties
- On the Hirzebruch–Kobayashi–Ono proportionality principle and the non-existence of compact solvable Clifford–Klein forms of certain homogeneous spaces
- The Lie group of vertical bisections of a regular Lie groupoid
- Chain conditions for graph C*-algebras
- Congruences in Hermitian Jacobi and Hermitian modular forms
- The Jensen–Pólya program for various L-functions
