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SPECIAL POINT PROBLEMS WITH ELLIPTIC MODULAR SURFACES

Part of: Model theory Arithmetic algebraic geometry

Published online by Cambridge University Press:  06 November 2013

Jonathan Pila
Jonathan Pila*
Affiliation:
Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG,U.K.
*
pila@maths.ox.ac.uk
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Abstract

We prove a “special point” result for products of elliptic modular surfaces, elliptic curves, multiplicative groups and complex lines, and deduce a result about vanishing linear combinations of singular moduli and roots of unity.

MSC classification

Secondary: 03C64: Model theory of ordered structures; o-minimality 11G18: Arithmetic aspects of modular and Shimura varieties

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Type
Research Article
Information
Mathematika , Volume 60 , Issue 1 , January 2014 , pp. 1 - 31
Copyright
Copyright © University College London 2013 

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