OFFSET
0,1
COMMENTS
The Pisot constant can be defined as the smallest number gamma such that, for all r < gamma, there exists a monic polynomial P with real coefficients such that |P(e^z)| <= 1 for all complex |z| <= r.
Pisot proves that if an entire function takes integer values at nonnegative integers and is O(e^(r*|z|)) for some r < gamma, then it is a finite sum of terms of the form z^n * alpha^z, where alpha is an algebraic integer and n is a nonnegative integer.
LINKS
Leonid V. Kovalev, Pisot constant beyond 0.843 (web.archive.org backup of web page no longer available as of Jan. 2021), June 17, 2017
Charles Pisot, Sur les fonctions arithmétiques analytiques à croissance exponentielle, Comptes rendus de l'Académie des Sciences Paris 222, (1946), pp. 988-990.
EXAMPLE
0.84383....
CROSSREFS
KEYWORD
AUTHOR
Charles R Greathouse IV, Mar 13 2018
STATUS
approved