Séminaire "Equations différentielles"
Some standard differential equations with irregular singularities, like Airy or Kloosterman and their symmetric products, behave in a way similar to Gauss-Manin differential equations , and their de Rham cohomology underlie a mixed Hodge structure, possibly with finite monodromy, enabling the use of tame arithmetic methods to handle the associated exponential sums. The talk will mainly focus on the Airy case, after a joint work with Jeng-Daw Yu.
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Vasily Golyshev & Vladimir Roubtsov