A note on circular distributions
Soogil Seo (2004)
Acta Arithmetica
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Soogil Seo (2004)
Acta Arithmetica
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Amir Akbary, Chantal David, Robert Juricevic (2004)
Acta Arithmetica
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Min Sha, Igor E. Shparlinski (2015)
Acta Arithmetica
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We obtain new results concerning the Lang-Trotter conjectures on Frobenius traces and Frobenius fields over single and double parametric families of elliptic curves. We also obtain similar results with respect to the Sato-Tate conjecture. In particular, we improve a result of A. C. Cojocaru and the second author (2008) towards the Lang-Trotter conjecture on average for polynomially parameterised families of elliptic curves when the parameter runs through a set of rational numbers of...
Kevin James, Gang Yu (2006)
Acta Arithmetica
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Ritabrata Munshi (2009)
Acta Arithmetica
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Jan Mikusiński, Roman Sikorski
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CONTENTS Introduction........................................................................................................... 3 § 1. The abstraction principle............................................................................... 4 § 2. Fundamental sequences of continuous functions......................................... 5 § 3. The definition of distributions........................................................................ 9 § 4. Distributions as a generalization of...
Matthev O. Ojo (2001)
Kragujevac Journal of Mathematics
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B. Kopociński, E. Trybusiowa (1966)
Applicationes Mathematicae
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Fabrizio Durante, Giovanni Puccetti, Matthias Scherer, Steven Vanduffel (2016)
Dependence Modeling
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A. Derdziński (1977)
Colloquium Mathematicae
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Grzegorz Łysik (1990)
Annales Polonici Mathematici
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Amílcar Pacheco (2010)
Acta Arithmetica
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Stevan Pilipović (1988)
Publications de l'Institut Mathématique
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Amílcar Pacheco (2003)
Acta Arithmetica
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Ricardo Estrada (2010)
Banach Center Publications
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It is well-known that any locally Lebesgue integrable function generates a unique distribution, a so-called regular distribution. It is also well-known that many non-integrable functions can be regularized to give distributions, but in general not in a unique fashion. What is not so well-known is that to many distributions one can associate an ordinary function, the function that assigns the distributional point value of the distribution at each point where the value exists, and that...
Bartosz Naskręcki (2016)
Banach Center Publications
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We discuss the distribution of Mordell-Weil ranks of the family of elliptic curves y² = (x + αf²)(x + βbg²)(x + γh²) where f,g,h are coprime polynomials that parametrize the projective smooth conic a² + b² = c² and α,β,γ are elements from ℚ̅. In our previous papers we discussed certain special cases of this problem and in this article we complete the picture by proving the general results.