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Session 1. Analytic Number Theory
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Diophantine equations in moderately many variables |
Oscar Marmon, Universität Göttingen, Germany
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We study the density of solutions to a general system of Diophantine
equations for which the underlying variety is a non-singular
complete intersection. The circle method gives precise information
about the density of solutions if the number of variables is large
enough in terms of the number of equations and their degree. We
derive upper bounds that are valid for a considerably smaller number
of variables, using a multidimensional q-analogue of van der Corput
differencing due to Heath-Brown.
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