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作者:Jason Bell , Rahim Moosa
来源:[J].Journal de théorie des nombres de Bordeaux, 2019, Vol.31 (1), pp.101-130
摘要:It is observed that Derksen’s Skolem–Mahler–Lech theorem is a special case of the isotrivial positive characteristic Mordell-Lang theorem due to the second author and Scanlon. This motivates an extension of the classical notion of a $k$-automatic subset of the natural n...
作者:Oleg Karpenkov , Matty van-Son
来源:[J].Journal de théorie des nombres de Bordeaux, 2019, Vol.31 (1), pp.131-144
摘要:In this paper, we generalize the Perron Identity for Markov minima. We express the values of binary quadratic forms with positive discriminant in terms of continued fractions associated to broken lines passing through the points where the values are computed.
作者:David Adam
来源:[J].Journal de théorie des nombres de Bordeaux, 2019, Vol.31 (1), pp.161-177
摘要:Let $q$ be an integer such that $|q|\ge 2$ and $s$ be a positive integer. In this article, we show that an entire function $f$ such that $\varlimsup _{r\rightarrow +\infty }\frac{\ln |f|_r}{\ln ^3r}<\frac{4s}{27\ln ^2|q|}$ and taking Gaussian integer values on $\lbrace q^m+i...
作者:Dragan Stankov
来源:[J].Journal de théorie des nombres de Bordeaux, 2019, Vol.31 (1), pp.215-226
摘要:We present a necessary and sufficient condition for a root greater than unity of a monic reciprocal polynomial of an even degree at least four, with integer coefficients, to be a Salem number. This condition requires that the minimal polynomial of some power of the algebraic inte...
作者:Solomon Vishkautsan
来源:[J].Journal de théorie des nombres de Bordeaux, 2019, Vol.31 (1), pp.49-79
摘要:We provide a complete classification of possible graphs of rational preperiodic points of quadratic rational functions defined over the rationals with a rational periodic critical point of period 3, under two assumptions: that these functions have no periodic points of period at ...
作者:Jędrzej Garnek
来源:[J].Journal de théorie des nombres de Bordeaux, 2019, Vol.31 (1), pp.227-242
摘要:Let $A$ be an abelian variety defined over a number field $K$. Fix a prime $p$ and a natural number $n$ and consider the field $K_n$, obtained by adjoining to $K$ all the coordinates of the $p^n$-torsion points of $A$. We give a lower bound on the $p$-part of the class group...
作者:Pierre Bel
来源:[J].Journal de théorie des nombres de Bordeaux, 2019, Vol.31 (1), pp.81-99
摘要:We give a sufficient condition on a rational $\alpha $ to get the irrationality of $\zeta _p(4, \alpha )$. In particular, for a prime $p\ge 19$, the number $\zeta _p(4, \frac{1}{p})$ is irrational. If this condition is satisfied, we give a bound for the irrationality measure of $...
作者:Jonathan Hickman , James Wright
来源:[J].Journal de théorie des nombres de Bordeaux, 2019, Vol.31 (1), pp.255-282
摘要:A sharp bound is obtained for the number of ways to express the monomial $X^n$ as a product of linear factors over $\mathbb{Z}/p^{\alpha }\mathbb{Z}$. The proof relies on an induction-on-scale procedure which is used to estimate the number of solutions to a certain system of poly...
作者:Félicien Comtat
来源:[J].Journal de théorie des nombres de Bordeaux, 2019, Vol.31 (1), pp.243-253
摘要:This paper is concerned with the density of rational points of bounded height lying on a variety defined by an integral quadratic form $Q$. In the case of four variables, we give an estimate that does not depend on the coefficients of $Q$. For more variables, a similar estimate s...
作者:Eryk Lipka
来源:[J].Journal de théorie des nombres de Bordeaux, 2019, Vol.31 (1), pp.283-291
摘要:In 2011 Deshouillers and Ruzsa [5] tried to argue that the sequence of the last nonzero digit of $n!$ in base 12 is not automatic. This statement was proven a few years later by Deshoulliers in [4]. In this paper we provide an alternate proof that lets us generalize the problem a...

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