edoc: No conditions. Results ordered -Date Deposited. 2024-11-07T16:33:40ZEPrintshttps://edoc.unibas.ch/images/uni-logo.jpghttps://edoc.unibas.ch/2021-11-03T16:02:30Z2021-11-03T16:02:30Zhttps://edoc.unibas.ch/id/eprint/78166This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/781662021-11-03T16:02:30ZGeneralized Vojta-Rémond inequalityFollowing and generalizing unpublished work of Ange, we prove a generalized version of Rémond's generalized Vojta inequality. This generalization can be applied to arbitrary products of irreducible positive-dimensional projective varieties, defined over the field of alge braic numbers, instead of powers of one fixed such variety. The proof runs closely along the lines of Rémond's proof. Gabriel A. Dill2021-11-01T15:05:16Z2021-11-01T15:05:16Zhttps://edoc.unibas.ch/id/eprint/78165This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/781652021-11-01T15:05:16ZUnlikely intersections with isogeny orbits in a product of elliptic schemesFix an elliptic curve Gabriel A. Dill2019-03-28T09:51:38Z2019-04-21T22:36:12Zhttps://edoc.unibas.ch/id/eprint/69956This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/699562019-03-28T09:51:38ZEffective approximation and Diophantine applicationsUsing the Thue-Siegel method, we obtain effective improvements on Liouville's irrationality measure for certain one-parameter families of algebraic numbers, defined by equations of the type (t-a)Q(t)+P(t)=0. We apply these to some corresponding Diophantine equations. We obtain bounds for the size of solutions, which depend polynomially on a, and bounds for the number of these solutions, which are independent of a and in some cases even independent of the degree of the equation. Gabriel Dill2017-10-13T09:54:19Z2017-10-13T09:54:19Zhttps://edoc.unibas.ch/id/eprint/53777This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/537772017-10-13T09:54:19ZEffective approximation and Diophantine applicationsUsing the Thue–Siegel method, we obtain effective improvements on Liouville’s irrationality measure for certain one-parameter families of algebraic numbers, defined by equations of the type $(t - a)Q(t) + P(t) = 0$. We apply these to some corresponding Diophantine equations. We obtain bounds for the size of solutions, which depend polynomially on $|a|$, and bounds for the number of these solutions, which are independent of $a$ and in some cases even independent of the degree of the equation. Gabriel A. Dill