PreprintarXiv licencearXiv
A proof of Karp's conjecture on the zeros of Toeplitz determinants of rising factorial series
Abstract
In 2012, D. Karp studied a family of polynomials constructed from Polya frequency sequences and conjectured that all their zeros are real and negative. We prove this conjecture for positive sequences and establish further results concerning the location of these zeros.
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BibTeX
@misc{zweiman2026proof,
title = {{A proof of Karp's conjecture on the zeros of Toeplitz determinants of rising factorial series}},
author = {Henry Zweiman},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18895},
eprint = {2610.18895},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18895},
}
RIS
TY - UNPB
TI - A proof of Karp's conjecture on the zeros of Toeplitz determinants of rising factorial series
AU - Henry Zweiman
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.18895
UR - https://arxiv.org/abs/2610.18895
AB - In 2012, D. Karp studied a family of polynomials constructed from Polya frequency sequences and conjectured that all their zeros are real and negative. We prove this conjecture for positive sequences and establish further results concerning the location of these zeros.
ER -