On the concentration of points on modular hyperbolas and exponential curves
Tsz Ho Chan, Igor E. Shparlinski (2010)
Acta Arithmetica
Similarity:
Tsz Ho Chan, Igor E. Shparlinski (2010)
Acta Arithmetica
Similarity:
Roland Matthes (1996)
Mathematische Zeitschrift
Similarity:
D. Choi (2006)
Acta Arithmetica
Similarity:
Heima Hayashi (2006)
Acta Arithmetica
Similarity:
Besser, Amnon (1997)
Documenta Mathematica
Similarity:
(2013)
Acta Arithmetica
Similarity:
The classical modular equations involve bivariate polynomials that can be seen to be univariate in the modular invariant j with integer coefficients. Kiepert found modular equations relating some η-quotients and the Weber functions γ₂ and γ₃. In the present work, we extend this idea to double η-quotients and characterize all the parameters leading to this kind of equation. We give some properties of these equations, explain how to compute them and give numerical examples.
Igor E. Shparlinski (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
Similarity:
For positive integers m, U and V, we obtain an asymptotic formula for the number of integer points (u,v) ∈ [1,U] × [1,V] which belong to the modular hyperbola uv ≡ 1 (mod m) and also have gcd(u,v) =1, which are also known as primitive points. Such points have a nice geometric interpretation as points on the modular hyperbola which are "visible" from the origin.
Hidegoro Nakano (1968)
Studia Mathematica
Similarity:
Özlem Imamoglu, Yves Martin (2006)
Acta Arithmetica
Similarity:
Carlo Bardaro, Ilaria Mantellini (2006)
Mathematica Slovaca
Similarity:
Serge Lang, Daniel S. Kubert (1978)
Mathematische Annalen
Similarity:
Hans Herda (1968)
Studia Mathematica
Similarity:
Wissam Raji (2007)
Acta Arithmetica
Similarity: