Diophantine properties of the zeros of certain Laguerre and para-Jacobi polynomials
Journal of Physics A: Mathematical and Theoretical, ISSN: 1751-8113, Vol: 45, Issue: 9
2012
- 11Citations
- 6Captures
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Article Description
Matrices A and B of arbitrary rank N, given by simple expressions in terms of the N zeros of certain Laguerre or para-Jacobi polynomials of degree N, feature a Diophantine property. In the Laguerre case, this property states that the 2N zeros of the polynomial p (Λ) = det[Λ + ΛA + B]are all integers; indeed we conjecture that det[Λ + ΛA + B]= Π [Λ ? k ]. The results in the para-Jacobi case are somewhat analogous; they refer to the zeros of the general solution of the ODE generally characterizing Jacobi polynomials, in the special case in which this solution is a para-Jacobi polynomial featuring an additional, arbitrary parameter. © 2012 IOP Publishing Ltd.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84857539689&origin=inward; http://dx.doi.org/10.1088/1751-8113/45/9/095207; https://iopscience.iop.org/article/10.1088/1751-8113/45/9/095207; https://dx.doi.org/10.1088/1751-8113/45/9/095207; https://hkvalidate.perfdrive.com/captcha?ssa=e4d4f473-f55e-401a-ad00-8bf19ee9fe8b&ssb=z61f1lplhdf1ezmeigdf4g2dm&ssc=https%3A%2F%2Fiopscience.iop.org%2Farticle%2F10.1088%2F1751-8113%2F45%2F9%2F095207&ssd=231757891615358&sse=deaaghcjgpogh@b&ssf=1e37337c6e0fc0e689e9d31ec53ae4dd07542093&ssg=4e75ebee-16d3-4207-a53e-10b8ef56a8bf&ssh=438ea540-b3b0-458e-8da3-388a0911e0b1&ssi=2ddfa03f-8427-408a-91a7-5f50ae003e90&ssj=9f139b34-79a6-4f99-932c-b5d8fdff6e15&ssk=support@shieldsquare.com&ssl=007003981057&ssm=159429860270707262545061137286797411&ssn=6426bc040aad6705cba85d9bf33a49e92d8b582aa583-e66a-4527-b0d802&sso=f0b625d2-51086ab3e700925e2dcaf7c49c8bb3daa230d8468626c5b6&ssp=35516865431587784644158887283452839&ssq=72400283653532106626136555374055418385484&ssr=NTIuMy4yMTcuMjU0&sss=Chrome/5.0%20(iPhone;%20U;%20CPU%20iPhone%20OS%203_0%20like%20Mac%20OS%20X;%20en-us)%20AppleWebKit/528.18%20(KHTML,%20like%20Gecko)%20Version/4.0%20Mobile/7A341%20Safari/528.16&sst=com.plumanalytics&ssu=Mozilla/5.0%20(compatible;%20Yahoo!%20Slurp;%20http://help.yahoo.com/help/us/ysearch/slurp)&ssv=ns1rl@pt9139t3s&ssw=&ssx=458424769752416&ssy=kkgebdbknggjhfmojlnm@o@mfd@oiif@khbgglop&ssz=a4266a8a3b73db4
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