### Department of Mathematics and Systems Analysis

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Dr. Tapani Matala-aho**Hermite-Thue Equation: Padé approximations and Siegels Lemma***** ** Wednesday 22 September 2021, 15:15, Zoom

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Padé approximations and Siegels lemma are widely used tools in Diophantine approximation theory. The appropriate homogeneous matrix equation representing both methods has an M x (L+1) coefficient matrix, where M≤L. Due to the Bombieri-Vaaler version of Siegels lemma, the upper bound of the minimal non-zero solution of the matrix equation can be improved by finding a big common factor of all the M x M minors of the coefficient matrix. We will present some key ingredients on how to find such a big common factor in the case of the exponential function. Further, in the case M=L, the existence of this common factor is a step towards understanding the nature of the twin type Hermite-Padé approximations to the exponential function. Joint work with Louna Seppälä.

ANTA Seminar

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