Lang-Trotter and Sato-Tate distributions in single and double parametric families of elliptic curves

• Autorzy: Min Sha , Igor E. Shparlinski
• Języki publikacji: EN

Abstrakty

EN

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 bounded height. Some of the families we consider are much thinner than the ones previously studied.

Kategorie tematyczne

• 11G20: Curves over finite and local fields
• 11B57: Farey sequences; the sequences 1 k , 2 k , ⋯
• 11G05: Elliptic curves over global fields
• 14H52: Elliptic curves

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 170
• Numer: 4
• Strony: 299-325

Daty

wydano

2015

Twórcy

autor

Min Sha

• School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia

autor

Igor E. Shparlinski

• School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia

Identyfikatory

DOI

10.4064/aa170-4-1