ON THE REDUCTION MODULO $p$ OF MAHLER EQUATIONS

DOI 8 References

Abstract

<p>The guiding thread of the present work is the following result, in the vain of Grothendieck’s conjecture for differential equations : if the reduction modulo almost all prime $p$ of a given linear Mahler equation with coefficients in $\mathbb{Q}(z)$ has a full set of algebraic solutions, then this equation has a full set of rational solutions. The proof of this result, given at the very end of the paper, relies on intermediate results of independent interest about Mahler equations in characteristic zero as well as in positive characteristic.</p>

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Details 詳細情報について

  • CRID
    1390573242839453440
  • DOI
    10.2748/tmj/1493172128
  • ISSN
    2186585X
    00408735
  • Text Lang
    en
  • Data Source
    • JaLC
    • Crossref
  • Abstract License Flag
    Disallowed

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