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Award ID contains: 1665115

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  1. (, ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE)
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  2. (, Matematičnì studìï)
    A solution of Problem 184 from the Scottish Book is given 
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  3. ; (, Journal d'Analyse Mathématique)
    We describe a new method of constructing transcendental entire functions A such that the differential equation w″ + Aw = 0 has two linearly independent solutions with relatively few zeros. In particular, we solve a problem of Bank and Laine by showing that there exist entire functions A of any prescribed order greater than 1/2 such that the differential equation has two linearly independent solutions whose zeros have finite exponent of convergence. We show that partial results by Bank, Laine, Langley, Rossi and Shen related to this problem are in fact best possible. We also improve a result of Toda and show that the estimate obtained is best possible. Our method is based on gluing solutions of the Schwarzian differential equation S(F) = 2A for infinitely many coefficients A. 
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  4. ; (, Symmetry, Integrability and Geometry: Methods and Applications)
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  5. ; (, Analysis and Mathematical Physics)
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  6. ; (, Journal of Mathematical Physics)
  7. ; (, International Mathematics Research Notices)
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  8. ; (, International Mathematics Research Notices)
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  9. ; (, Communications in Mathematical Physics)
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  10. ; ; (, Mathematical Proceedings of the Cambridge Philosophical Society)
    Abstract We study entire functions whose zeros and one-points lie on distinct finite systems of rays. General restrictions on these rays are obtained. Non-trivial examples of entire functions with zeros and one-points on different rays are constructed, using the Stokes phenomenon for second order linear differential equations. 
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