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The retrieval of a rotation invariant distribution of (X, Y) from E(X2 | Y)

✍ Scribed by Gérard Letac

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
280 KB
Volume
63
Category
Article
ISSN
0378-3758

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✦ Synopsis

Suppose that the distribution of (X, Y) in N2 is rotation invariant. Then, if the density h .of X is such that ~(X 2) is finite and iff(y

This formula has been already obtained in 1986 by Pawel J. Szablowski; we offer two proofs: one using characteristic functions, and the other as a corollary of a more general result on beta distributions. ~) 1997 Elsevier Science B.V.

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This paper continues the investigation of the arithmetic of the curves C A : y 2 =x a +A and their Jacobians J A , where a is an odd prime and A is an integer not divisible by a, which was begun in an earlier paper. In the first part, we sketch how to extend the formula for the dimension of a certai