On the Euler Function on Differences Between the Coordinates of Points on Modular Hyperbolas
Igor E. Shparlinski
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008), p. 1-7 / Harvested from The Polish Digital Mathematics Library
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For a prime p > 2, an integer a with gcd(a,p) = 1 and real 1 ≤ X,Y < p, we consider the set of points on the modular hyperbola a,p(X,Y)=(x,y):xy≡a(modp),1≤x≤X,1≤y≤Y. We give asymptotic formulas for the average values ∑(x,y)∈a,p(X,Y)x≠y*φ(|x-y|)/|x-y| and ∑(x,y)∈a,p(X,X)x≠y*φ(|x-y|) with the Euler function φ(k) on the differences between the components of points of a,p(X,Y).

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:281163 
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     title = {On the Euler Function on Differences Between the Coordinates of Points on Modular Hyperbolas},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     volume = {56},
     year = {2008},
     pages = {1-7},
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     language = {en},
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Igor E. Shparlinski. On the Euler Function on Differences Between the Coordinates of Points on Modular Hyperbolas. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) pp. 1-7. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-1-1/