We derived an asymptotic formula for the number of pairs of integers which are mutually square. Earlier results dealt with pairs of integers subject to the restriction that they are both odd, co-prime and square-free. Here we remove all these restrictions and prove (similar to the best known one with restirctions) that number of such pair of integers upto a large real X is asymptotic to cX^2/ log X with an absolute constant c which we give explicitly. Our error term is also compatible to the best known one.
Kalyan, C., Jorge, J.U., Pappalardi, F. (2017). Pairs of integers which are mutually squares. SCIENCE CHINA. MATHEMATICS, 70(9), 1633-1649 [10.1007/s11425-016-0343-1].
Pairs of integers which are mutually squares
PAPPALARDI, FRANCESCO
2017
Abstract
We derived an asymptotic formula for the number of pairs of integers which are mutually square. Earlier results dealt with pairs of integers subject to the restriction that they are both odd, co-prime and square-free. Here we remove all these restrictions and prove (similar to the best known one with restirctions) that number of such pair of integers upto a large real X is asymptotic to cX^2/ log X with an absolute constant c which we give explicitly. Our error term is also compatible to the best known one.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
