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Supersingular abelian surfaces and Eichler class number formula
Let be a totally real field with ring of integers , and be a
totally definite quaternion algebra over . A well-known formula established
by Eichler and then extended by K\"orner computes the class number of any
-order in . In this paper we generalize the Eichler class number
formula so that it works for arbitrary -orders in . The
motivation is to count the isomorphism classes of supersingular abelian
surfaces in a simple isogeny class over a prime finite field . We
give explicit formulas for the number of these isomorphism classes for all
primes .Comment: 29 pages, 3 numerical tables, shortened revised version with same
results, Sections 7-9 of v2 are remove
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