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A conjecture on the zeta functions of pairs of ternary quadratic forms
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 143, Number 2, April 2021
- pp. 335-410
- 10.1353/ajm.2021.0010
- Article
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abstract:
We consider the prehomogeneous vector space of pairs of ternary quadratic forms. For the lattice of pairs of integral ternary quadratic forms and its dual lattice, there are six zeta functions associated with the the prehomogeneous vector space. We present a conjecture which states that there are simple relations among the six zeta functions. We prove that the coefficients coincide on fundamental discriminants.