Displaying similar documents to “On the set of distances between two sets over finite fields.”

Heights, regulators and Schinzel's determinant inequality

Shabnam Akhtari, Jeffrey D. Vaaler (2016)

Acta Arithmetica

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We prove inequalities that compare the size of an S-regulator with a product of heights of multiplicatively independent S-units. Our upper bound for the S-regulator follows from a general upper bound for the determinant of a real matrix proved by Schinzel. The lower bound for the S-regulator follows from Minkowski's theorem on successive minima and a volume formula proved by Meyer and Pajor. We establish similar upper bounds for the relative regulator of an extension l/k of number fields. ...

On the number of rational points of Jacobians over finite fields

Philippe Lebacque, Alexey Zykin (2015)

Acta Arithmetica

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We prove lower and upper bounds for the class numbers of algebraic curves defined over finite fields. These bounds turn out to be better than most of the previously known bounds obtained using combinatorics. The methods used in the proof are essentially those from the explicit asymptotic theory of global fields. We thus provide a concrete application of effective results from the asymptotic theory of global fields and their zeta functions.

Schanuel Nullstellensatz for Zilber fields

Paola D'Aquino, Angus Macintyre, Giuseppina Terzo (2010)

Fundamenta Mathematicae

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We characterize the unsolvable exponential polynomials over the exponential fields introduced by Zilber, and deduce Picard's Little Theorem for such fields.

On the Gibson Bounds over Finite Fields

V. Budrevich, Mikhail, E. Guterman, Alexander (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 15A15, 15A04. We investigate the Pólya problem on the sign conversion between the permanent and the determinant over finite fields. The main attention is given to the sufficient conditions which guarantee non-existence of sing-conversion. In addition we show that F3 is the only field with the property that any matrix with the entries from the field is convertible. As a result we obtain that over finite fields there are no analogs of...