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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

H. L. Resnikoff  and
R. L. Saldaña
H. L. Resnikoff
Affiliation:
Rice University, Houston, Texas 77001, U.S.A.
R. L. Saldaña
Affiliation:
Rice University, Houston, Texas 77001, U.S.A.
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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

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 16 , Issue 2 , September 1975 , pp. 69 - 87
Copyright
Copyright © Glasgow Mathematical Journal Trust 1975

References

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