Department of Mathematics and Statistics
Bar-Ilan University
Mathematics Colloquium
Dr. A. J. Kanel-Belov
International University of Bremen
Exponential diophantine equations over a field of positive
characteristic and Taylor series of algebraic functions
Sunday, 29 December 2002
12:00 pm (Light refreshments served at 11:45 am)
Abstract: Consider a system of exponential algebraic equations in s
variables n_1,...,n_s (appearing as exponents) with polynomial
coefficients. According to a result of J. Robinson, algorithmic questions
concerning the existence of solutions of such systems are unsolvable.
However, if the each base of the exponents belongs to a field of
characteristic p>0, then there exists an algorithm describing all
solutions of such systems in terms of p-adic presentations of the
unknowns. Similar results involve Taylor series of algebraic functions.
This subject seems to be closely related to the Weil conjecture proved by
P. Deligne.
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