Abstract
For a given real entire function φ in the class U *2n , n ≥ 0, with finitely many nonreal zeroes, we establish a connection between the number of real zeroes of the functions Q[φ] = (φ′/φ)′ and Q 1[φ] = (φ″/φ′)′. This connection leads to a proof of the Hawaii Conjecture (T. Craven, G. Csordas, and W. Smith [5]), which states that if φ is a real polynomial, then the number of real zeroes of Q[φ] does not exceed the number of nonreal zeroes of φ.
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Dedicated with gratitude to Thomas Craven, George Csordas, and Wayne Smith.
This work was supported by the Sofja Kovalevskaja Research Prize of Alexander von Humboldt Foundation.
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Tyaglov, M. On the number of real critical points of logarithmic derivatives and the Hawaii conjecture. JAMA 114, 1–62 (2011). https://doi.org/10.1007/s11854-011-0011-1
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DOI: https://doi.org/10.1007/s11854-011-0011-1