Geodesic
Diophantine equations in semiprimes
Discrete analysis (2019) Cet article a éte moissonné depuis la source Scholastica

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A semiprime is a natural number which is the product of two (not necessarily distinct) prime numbers. Let $F(x_1, \ldots, x_n)$ be a degree $d$ homogeneous form with integer coefficients. We provide sufficient conditions, similar to those of the seminal work of B. J. Birch, for which the equation $F (x_1, \ldots, x_n) = 0$ has infinitely many integer solutions with semiprime coordinates. Previously it was known, by a result of Á. Magyar and T. Titichetrakun, that under the same hypotheses there exist infinitely many integer solutions to the equation with coordinates that have at most $384 n^{3/2} d (d+1)$ prime factors.
Publié le : 
@article{DAS_2019_a3,
     author = {Shuntaro Yamagishi},
     title = {Diophantine equations in semiprimes},
     journal = {Discrete analysis},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2019_a3/}
}
TY  - JOUR
AU  - Shuntaro Yamagishi
TI  - Diophantine equations in semiprimes
JO  - Discrete analysis
PY  - 2019
UR  - http://geodesic.mathdoc.fr/item/DAS_2019_a3/
LA  - en
ID  - DAS_2019_a3
ER  - 
%0 Journal Article
%A Shuntaro Yamagishi
%T Diophantine equations in semiprimes
%J Discrete analysis
%D 2019
%U http://geodesic.mathdoc.fr/item/DAS_2019_a3/
%G en
%F DAS_2019_a3
Shuntaro Yamagishi. Diophantine equations in semiprimes. Discrete analysis (2019). http://geodesic.mathdoc.fr/item/DAS_2019_a3/