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An analogue of a conjecture of Sato and Tate for a Hilbert modular form
Published online by Cambridge University Press: 18 May 2009
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If k denotes a number field and εm is the product of an elliptic curve ε with itself m times over k, then for each prime π where ε has non-degenerate reduction, the zeta factor ζ(επ'S) can be expressed as
Where |π| denotes the norm of π. It is a consequence of a conjecture of Tate [16] that if ε does not have complex multiplications, then the numbers are distributed according to the density function
that is, the density of the set of primes π such that – is
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