We present two generalizations of Roth's approximation theorem on proper adelic curves, assuming some technical conditions on the behavior of the logarithmic absolute values. We illustrate how tightening such assumptions makes our inequalities stronger. As special cases, we recover Corvaja's results for fields admitting a product formula and Vojta's ones for arithmetic function fields.
On the generalization of Roth's theorem
Zucconi F.
2025-01-01
Abstract
We present two generalizations of Roth's approximation theorem on proper adelic curves, assuming some technical conditions on the behavior of the logarithmic absolute values. We illustrate how tightening such assumptions makes our inequalities stronger. As special cases, we recover Corvaja's results for fields admitting a product formula and Vojta's ones for arithmetic function fields.File in questo prodotto:
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