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.
On the classification of rank-two representations of quasiprojective fundamental groups
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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.