A324794 Conjectured value of N(2^n), defined by property that the Jensen polynomial J^{2^n,m}_p(X) is hyperbolic for m >= N(2^n).

1, 25, 206, 1269, 6917, 35627

Offset

0,2

Comments

Normally the OEIS does not list conjectured values in the Data section, but an exception has been made here in view of the importance of these numbers.

The conjectured values of N(d) for d = 1,...,9 are 1, 25, 94, 206, 381, 610, 908, 1269, 1701.

See Larson-Wagner (2019) for the proof that certain of these numbers are correct.

References

Ken Ono, Jensen-Polya Program for the Riemann Hypothesis and Related Problems, Colloquium Lecture, Mathematics Department, Rutgers University, Piscataway, NJ, Sep 06 2019.

Links

Table of n, a(n) for n=0..5.

M. Griffin, K. Ono, L. Rolen, and D. Zagier, Jensen polynomials for the Riemann zeta function and other sequences, arXiv:1902.07321 [math.NT], 2019.

M. Griffin, K. Ono, L. Rolen, and D. Zagier, Jensen polynomials for the Riemann zeta function and other sequences, Proceedings of the National Academy of Sciences, 116(23) (2019), 11103-11110.

H. Larson and I. Wagner, Hyperbolicity of the partition Jensen polynomials, arXiv:1904.12727 [math.NT], 2019.

H. Larson and I. Wagner, Hyperbolicity of the partition Jensen polynomials, Res. Numb. Th. 5(2) (2019), Art. 19, 12 pp. (Correction, Res. Numb. Th. 5(3) (2019), Art. 21, 1 p.)

Ken Ono, Jensen-Polya Program for the Riemann Hypothesis and Related Problems, Oregon Number Theory Days (Colloquium Lecture), Oregon State University, Winter 2018.

Crossrefs

Sequence in context: A220677 A125362 A126520 * A348201 A264493 A224419

Adjacent sequences: A324791 A324792 A324793 * A324795 A324796 A324797

Keyword

nonn,hard,more

Author

N. J. A. Sloane, Sep 07 2019

Status

approved