Algebraic A-hypergeometric functions


We formulate and prove a combinatorial criterion to decide if an A-hypergeometric system of differential equations has a full set of algebraic solutions or not. This criterion generalises the so-called interlacing criterion in the case of hypergeometric functions of one variable.


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Correspondence to Frits Beukers.

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Beukers, F. Algebraic A-hypergeometric functions. Invent. math. 180, 589–610 (2010).

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  • Hypergeometric Function
  • Polynomial Solution
  • Algebraic Solution
  • Hypergeometric Equation
  • Fuchsian System