Linear independence of 'logarithms' in linear varieties
On an equation in cyclotomic numbers
On polynomials taking small values at integral arguments
Local-global divisibility of rational points in some commutative algebraic groups
Let be a commutative algebraic group defined over a number field . We consider the following question:A complete answer for the case of the multiplicative group is classical. We study other instances and in particular obtain an affirmative answer when is a prime and is either an elliptic curve or a torus of small dimension with respect to . Without restriction on the dimension of a torus, we produce an example showing that the answer can be negative even when is a prime.
Two problems related to the non-vanishing of
We study two rather different problems, one arising from Diophantine geometry and one arising from Fourier analysis, which lead to very similar questions, namely to the study of the ranks of matrices with entries either zero or , where denotes the “centered” fractional part of . These ranks, in turn, are closely connected with the non-vanishing of the Dirichlet -functions at .
Number fields with the same index
Decomposition of primes in non-maximal orders
On polynomials taking small values at integral arguments II
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