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Search: MSC category 11R52 ( Quaternion and other division algebras: arithmetic, zeta functions )

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1. CJM Online first

Martin, Kimball
Congruences for modular forms mod 2 and quaternionic $S$-ideal classes
We prove many simultaneous congruences mod 2 for elliptic and Hilbert modular forms among forms with different Atkin--Lehner eigenvalues. The proofs involve the notion of quaternionic $S$-ideal classes and the distribution of Atkin--Lehner signs among newforms.

Keywords:modular forms, congruences, quaternion algebras
Categories:11F33, 11R52

2. CJM 1999 (vol 51 pp. 10)

Chacron, M.; Tignol, J.-P.; Wadsworth, A. R.
Tractable Fields
A field $F$ is said to be tractable when a condition described below on the simultaneous representation of quaternion algebras holds over $F$. It is shown that a global field $F$ is tractable i{f}f $F$ has at most one dyadic place. Several other examples of tractable and nontractable fields are given.

Categories:12E15, 11R52

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