scholarly journals Solutions of KZ differential equations modulo p

2018 ◽  
Vol 48 (3) ◽  
pp. 655-683 ◽  
Author(s):  
Vadim Schechtman ◽  
Alexander Varchenko
Keyword(s):  
Differential Equations ◽  
Modulo P

scholarly journals Reduction modulo p of differential equations

1996 ◽  
Vol 7 (3) ◽  
pp. 367-387 ◽  
Author(s):  
Marius van der Put
Keyword(s):  
Differential Equations ◽  
Reduction Modulo ◽  
Modulo P

On the Local Structure of Mahler Systems

2020 ◽  
Author(s):  
Julien Roques
Keyword(s):  
Differential Equations ◽  
Local Structure ◽  
Alternative Proof ◽  
Reduction Modulo ◽  
Modulo P ◽  
Almost All ◽  
The Given ◽  
Algebraic Solutions

Abstract This paper is a 1st step in the direction of a better understanding of the structure of the so-called Mahler systems: we classify these systems over the field $\mathscr{H}$ of Hahn series over $\overline{{\mathbb{Q}}}$ and with value group ${\mathbb{Q}}$. As an application of (a variant of) our main result, we give an alternative proof of the following fact: if, for almost all primes $p$, the reduction modulo $p$ of a given Mahler equation with coefficients in ${\mathbb{Q}}(z)$ has a full set of algebraic solutions over $\mathbb{F}_{p}(z)$, then the given equation has a full set of solutions in $\overline{{\mathbb{Q}}}(z)$ (this is analogous to Grothendieck’s conjecture for differential equations).

Partial Differential Equations

2020 ◽  
Author(s):  
A. K. Nandakumaran ◽  
P. S. Datti
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential
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