122 citations
- Carleton UniversityCA2 papers
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- École Polytechnique Fédérale de LausanneCH2 papers
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- Université de MontréalCA2 papers
- Chiba UniversityJP1 paper
- Dalhousie UniversityCA1 paper
- Georgia Institute of TechnologyUS1 paper
- Institut de recherche mathématique de RennesFR1 paper
- Institute of SpectroscopyRU1 paper
- Kharkiv Institute of Physics and TechnologyUA1 paper
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7 papers · 1 filter
Nonexistence of permutation binomials of certain shapes
Ariane M. Masuda, Michael E. Zieve
Suppose x^m + c*x^n is a permutation polynomial over GF(p), where p>5 is prime, m>n>0, and c is in GF(p)^*. We prove that gcd(m-n,p-1) is not 2 or 4. In the special case that eithe…
A discrete mean value of the derivative of the Riemann zeta function
Nathan Ng
In this article we compute a discrete mean value of the derivative of the Riemann zeta function. This mean value will be important for several applications concerning the size of $…
Rational functions with linear relations
Ariane M. Masuda, Michael E. Zieve
We find all polynomials f,g,h over a field K such that g and h are linear and f(g(x))=h(f(x)). We also solve the same problem for rational functions f,g,h, in case the field K is a…
A Gel'fond type criterion in degree two
Benoit Arbour, Damien Roy
We establish a criterion for a complex number to be algebraic over Q of degree at most two. It requires that, for any sufficiently large real number X, there exists a non-zero poly…
Approximation simultanée d'un nombre et de son carré [Simultaneous approximation to a real number and its square]
Damien Roy
In 1969, H. Davenport and W. Schmidt established a measure of simultaneous approximation for a real number ξand its square by rational numbers with the same denominator, assuming o…
Approximation to real numbers by cubic algebraic integers II
Damien Roy
It has been conjectured for some time that, for any integer n\ge 2, any real number ε>0 and any transcendental real number ξ, there would exist infinitely many algebraic integers α…