Hankel Determinants of Zeta Values
We study the asymptotics of Hankel determinants constructed using the values ζ(an+b) of the Riemann zeta function at positive integers in an arithmetic progression. Our principal result is a Diophantine application of the asymptotics.
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2015 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147145 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Hankel Determinants of Zeta Values / A. Haynes, W. Zudilin // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862705325464879104 |
|---|---|
| author | Haynes, A. Zudilin, W. |
| author_facet | Haynes, A. Zudilin, W. |
| citation_txt | Hankel Determinants of Zeta Values / A. Haynes, W. Zudilin // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study the asymptotics of Hankel determinants constructed using the values ζ(an+b) of the Riemann zeta function at positive integers in an arithmetic progression. Our principal result is a Diophantine application of the asymptotics.
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| first_indexed | 2025-12-07T16:54:18Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147145 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:54:18Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Haynes, A. Zudilin, W. 2019-02-13T17:27:36Z 2019-02-13T17:27:36Z 2015 Hankel Determinants of Zeta Values / A. Haynes, W. Zudilin // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 6 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 11J72; 11C20; 11M06; 41A60 DOI:10.3842/SIGMA.2015.101 https://nasplib.isofts.kiev.ua/handle/123456789/147145 We study the asymptotics of Hankel determinants constructed using the values ζ(an+b) of the Riemann zeta function at positive integers in an arithmetic progression. Our principal result is a Diophantine application of the asymptotics. This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications.
 The full collection is available at http://www.emis.de/journals/SIGMA/OPSFA2015.html.
 We would like to thank the anonymous referees for their healthy criticism on the earlier draft of
 the note. Research of first author (Alan Haynes) was supported by EPSRC grants EP/L001462,
 EP/J00149X, EP/M023540. Research of second author (Wadim Zudilin) was supported by
 Australian Research Council grant DP170100466. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Hankel Determinants of Zeta Values Article published earlier |
| spellingShingle | Hankel Determinants of Zeta Values Haynes, A. Zudilin, W. |
| title | Hankel Determinants of Zeta Values |
| title_full | Hankel Determinants of Zeta Values |
| title_fullStr | Hankel Determinants of Zeta Values |
| title_full_unstemmed | Hankel Determinants of Zeta Values |
| title_short | Hankel Determinants of Zeta Values |
| title_sort | hankel determinants of zeta values |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147145 |
| work_keys_str_mv | AT haynesa hankeldeterminantsofzetavalues AT zudilinw hankeldeterminantsofzetavalues |