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1. CJM 2003 (vol 55 pp. 432)
Pair Correlation of Squares in $p$-Adic Fields Let $p$ be an odd prime number, $K$ a $p$-adic field of degree $r$
over $\mathbf{Q}_p$, $O$ the ring of integers in $K$, $B = \{\beta_1,\dots,
\beta_r\}$ an integral basis of $K$ over $\mathbf{Q}_p$, $u$ a unit in $O$
and consider sets of the form $\mathcal{N}=\{n_1\beta_1+\cdots+n_r\beta_r:
1\leq n_j\leq N_j, 1\leq j\leq r\}$. We show under certain growth
conditions that the pair correlation of $\{uz^2:z\in\mathcal{N}\}$ becomes
Poissonian.
Categories:11S99, 11K06, 1134 |
2. CJM 2000 (vol 52 pp. 47)
Comparison of $K$-Theory Galois Module Structure Invariants We prove that two, apparently different, class-group valued Galois
module structure invariants associated to the algebraic $K$-groups
of rings of algebraic integers coincide. This comparison result is
particularly important in making explicit calculations.
Categories:11S99, 19F15, 19F27 |