Geodesic
Lang–Trotter and Sato–Tate distributions in single and double parametric families of elliptic curves
Min Sha 1   ; Igor E. Shparlinski 1
1 School of Mathematics and Statistics University of New South Wales Sydney, NSW 2052, Australia
Acta Arithmetica, Tome 170 (2015) no. 4, pp. 299-325 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 bounded height. Some of the families we consider are much thinner than the ones previously studied.
DOI : 10.4064/aa170-4-1
Keywords: obtain results concerning lang trotter conjectures frobenius traces frobenius fields single double parametric families elliptic curves obtain similar results respect sato tate conjecture particular improve result nbsp nbsp cojocaru second author towards lang trotter conjecture average polynomially parameterised families elliptic curves parameter runs through set rational numbers bounded height families consider much thinner previously studied

Min Sha  1   ; Igor E. Shparlinski  1

1 School of Mathematics and Statistics University of New South Wales Sydney, NSW 2052, Australia 
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     title = {Lang{\textendash}Trotter and {Sato{\textendash}Tate} distributions in single and double parametric families of elliptic curves},
     journal = {Acta Arithmetica},
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Min Sha; Igor E. Shparlinski. Lang–Trotter and Sato–Tate distributions in single and double parametric families of elliptic curves. Acta Arithmetica, Tome 170 (2015) no. 4, pp. 299-325. doi: 10.4064/aa170-4-1

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