On the Euler Function on Differences Between the Coordinates of Points on Modular Hyperbolas

• Autorzy: Igor E. Shparlinski
• Języki publikacji: EN

Abstrakty

EN

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
$𝓗_{a,p}(X,Y) = {(x,y) : xy ≡ a(mod p), 1 ≤x≤X, 1 ≤y≤Y}$.
We give asymptotic formulas for the average values
$∑_{\substack (x,y)∈ 𝓗_{a,p}(X,Y) x ≠ y*} φ(|x-y|)/|x-y|$ and $∑_{\substack (x,y)∈ 𝓗_{a,p}(X,X) x ≠ y*} φ(|x-y|)$
with the Euler function φ(k) on the differences between the components of points of $𝓗_{a,p}(X,Y)$.

Kategorie tematyczne

• 11N25: Distribution of integers with specified multiplicative constraints
• 11K38: Irregularities of distribution, discrepancy
• 11A07: Congruences; primitive roots; residue systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2008
• Tom: 56
• Numer: 1
• Strony: 1-7

Daty

wydano

2008

Twórcy

autor

Igor E. Shparlinski

• Department of Computing, Macquarie University, North Ryde, NSW 2109, Australia

Identyfikatory

DOI

10.4064/ba56-1-1