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Pairs of integers which are mutually squares

Autor
Chakraborty, K.; Jimenez, J.; Pappalardi, F.
Tipus d'activitat
Article en revista
Revista
Science China Mathematics
Data de publicació
2017-09
Volum
60
Número
9
Pàgina inicial
1633
Pàgina final
1646
DOI
https://doi.org/10.1007/s11425-016-0343-1 Obrir en finestra nova
URL
http://link.springer.com/article/10.1007%2Fs11425-016-0343-1 Obrir en finestra nova
Resum
We derived an asymptotic formula for the number of pairs of integers which are mutually squares. Earlier results dealt with pairs of integers subject to the restriction that they are both odd, co-prime and squrefree. Here we remove all these restrictions and prove (similar to the best known one with restrictions) that the number of such pair of integers upto a large real X is asymptotic to cX2logX with an absolute constant c which we give explicitly. Our error term is also compatible to the best...
Paraules clau
Jacobi symbol, mutually squares, quadratic reciprocity
Grup de recerca
TN - Grup de Recerca en Teoria de Nombres

Participants