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SUMMARY:Thu Hien Nguyen (Leipzig University\, Germany & V. N. Karazin Khar
 kiv University\, Ukraine)
DTSTART:20230425T130000Z
DTEND:20230425T140000Z
DTSTAMP:20260422T201846Z
UID:CAvid/102
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/102/">
 Some results on entire functions from the Laguerre-Pólya class: proof ide
 as and techniques</a>\nby Thu Hien Nguyen (Leipzig University\, Germany & 
 V. N. Karazin Kharkiv University\, Ukraine) as part of CAvid: Complex Anal
 ysis video seminar\n\nLecture held in N/A.\n\nAbstract\nThe Laguerre-P\\'o
 lya class is a class of entire functions that are locally the uniform limi
 t of a sequence of real polynomials that have only real zeros.  We present
  some simple necessary and sufficient conditions for entire functions to b
 elong to the Laguerre–Pólya class in terms of their Taylor coefficients
 .  For an entire function $f(z) = \\sum_{k=0}^{\\infty} a_k z^k$\, we defi
 ne the second quotients of Taylor coefficients as $q_n(f) := \\frac{a_{n-1
 }^2}{a_{n-2}  a_{n}}$\,  $n\\geq 2$\, and find conditions on $q_n(f)$ for 
 $f$ to belong to  the Laguerre--P\\'olya class\, or to have only real zero
 s.  In this talk\, we will focus on the entire functions with increasing s
 econd quotients of Taylor coefficients\, and discuss proof ideas and techn
 iques we used. \n \n This is joint work with Anna Vishnyakova.\n
LOCATION:https://researchseminars.org/talk/CAvid/102/
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