G-functions of order two exist that are not polynomial expressions in algebraic pullbacks of hypergeometric functions, answering Siegel's problem negatively and adding counterexamples to Dwork's conjecture.
G -functions and geometry , volume E13 of Aspects of Mathematics
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On Siegel's problem and Dwork's conjecture for $G$-functions
G-functions of order two exist that are not polynomial expressions in algebraic pullbacks of hypergeometric functions, answering Siegel's problem negatively and adding counterexamples to Dwork's conjecture.