Geodesic
Zeros, growth and Taylor coefficients of entire solutions of linear q-difference equations
Walter Bergweiler1
1 Christian-Albrechts-Universität zu Kiel, Mathematisches Seminar
Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 249-277

Voir la notice de l'article provenant de la source Journal.fi

We consider transcendental entire solutions of linear $q$-difference equations with polynomial coefficients and determine the asymptotic behavior of their Taylor coefficients. We use this to show that under a suitable hypothesis on the associated Newton-Puiseux diagram their zeros are asymptotic to finitely many geometric progressions. We also sharpen previous results on the growth rate of entire solutions.
Keywords: Difference equation, q-difference equation, entire function, maximum modulus, growth, zeros, Taylor series, Newton-Puiseux diagram

Walter Bergweiler 1

1 Christian-Albrechts-Universität zu Kiel, Mathematisches Seminar 
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Walter Bergweiler. Zeros, growth and Taylor coefficients of entire solutions of  linear q-difference equations. Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 249-277. http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a13/