The Number of Zeros in a Disk of a Complex Polynomial with Coefficients Satisfying Various Monotonicity Conditions
Motivated by results on the location of the zeros of a complex polynomial with monotonicity conditions on the coefficients (such as the classical Eneström–Kakeya theorem and its recent generalizations), we impose similar conditions and give bounds on the number of zeros in certain regions. We do so...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | AppliedMath |
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| Online Access: | https://www.mdpi.com/2673-9909/3/4/38 |
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| author | Robert Gardner Matthew Gladin |
| author_facet | Robert Gardner Matthew Gladin |
| author_sort | Robert Gardner |
| collection | DOAJ |
| description | Motivated by results on the location of the zeros of a complex polynomial with monotonicity conditions on the coefficients (such as the classical Eneström–Kakeya theorem and its recent generalizations), we impose similar conditions and give bounds on the number of zeros in certain regions. We do so by introducing a reversal in monotonicity conditions on the real and imaginary parts of the coefficients and also on their moduli. The conditions imposed are less restrictive than many of those in the current literature and hence apply to polynomials not covered by previous results. The results presented naturally apply to certain classes of lacunary polynomials. In particular, the results apply to certain polynomials with two gaps in their coefficients. |
| first_indexed | 2024-03-08T21:02:39Z |
| format | Article |
| id | doaj.art-7a45538608ba4efcbca0a8b72bf1b48b |
| institution | Directory Open Access Journal |
| issn | 2673-9909 |
| language | English |
| last_indexed | 2024-03-08T21:02:39Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | AppliedMath |
| spelling | doaj.art-7a45538608ba4efcbca0a8b72bf1b48b2023-12-22T13:48:46ZengMDPI AGAppliedMath2673-99092023-10-013472272910.3390/appliedmath3040038The Number of Zeros in a Disk of a Complex Polynomial with Coefficients Satisfying Various Monotonicity ConditionsRobert Gardner0Matthew Gladin1Department of Mathematics and Statistics, East Tennessee State University, Johnson City, TN 37614, USADepartment of Mathematics and Statistics, East Tennessee State University, Johnson City, TN 37614, USAMotivated by results on the location of the zeros of a complex polynomial with monotonicity conditions on the coefficients (such as the classical Eneström–Kakeya theorem and its recent generalizations), we impose similar conditions and give bounds on the number of zeros in certain regions. We do so by introducing a reversal in monotonicity conditions on the real and imaginary parts of the coefficients and also on their moduli. The conditions imposed are less restrictive than many of those in the current literature and hence apply to polynomials not covered by previous results. The results presented naturally apply to certain classes of lacunary polynomials. In particular, the results apply to certain polynomials with two gaps in their coefficients.https://www.mdpi.com/2673-9909/3/4/38complex polynomialscounting zerosmonotone coefficients |
| spellingShingle | Robert Gardner Matthew Gladin The Number of Zeros in a Disk of a Complex Polynomial with Coefficients Satisfying Various Monotonicity Conditions AppliedMath complex polynomials counting zeros monotone coefficients |
| title | The Number of Zeros in a Disk of a Complex Polynomial with Coefficients Satisfying Various Monotonicity Conditions |
| title_full | The Number of Zeros in a Disk of a Complex Polynomial with Coefficients Satisfying Various Monotonicity Conditions |
| title_fullStr | The Number of Zeros in a Disk of a Complex Polynomial with Coefficients Satisfying Various Monotonicity Conditions |
| title_full_unstemmed | The Number of Zeros in a Disk of a Complex Polynomial with Coefficients Satisfying Various Monotonicity Conditions |
| title_short | The Number of Zeros in a Disk of a Complex Polynomial with Coefficients Satisfying Various Monotonicity Conditions |
| title_sort | number of zeros in a disk of a complex polynomial with coefficients satisfying various monotonicity conditions |
| topic | complex polynomials counting zeros monotone coefficients |
| url | https://www.mdpi.com/2673-9909/3/4/38 |
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