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AUTOMATA AND TRANSCENDENCE OF THE TATE PERIOD IN FINITE CHARACTERISTIC
 

Summary: AUTOMATA AND TRANSCENDENCE OF THE TATE PERIOD
IN FINITE CHARACTERISTIC
JEAN­PAUL ALLOUCHE & DINESH S. THAKUR*
Abstract: Using the techniques of automata theory, we give another proof of
the function field analogue of Mahler­Manin conjecture and prove transcendence
results for the power series associated to higher divisor functions oe k (n) =
P
djn d k
Let p be a prime number, and k be an algebraic closure of F p . Let q be a variable
and consider a 4 ; a 6 2 k[[q]] defined by
a 4 :=
X
n–1
\Gamma5n 3 q n
1 \Gamma q n
; a 6 :=
X
n–1
\Gamma(7n 5 + 5n 3 )q n
12(1 \Gamma q n ) :

  

Source: Allouche, Jean-Paul - Laboratoire de Recherche en Informatique, Université de Paris-Sud 11

 

Collections: Computer Technologies and Information Sciences