The (α, β)-ramification invariants of a number field
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Abstract Let L be a number field. For a given prime p, we define integers α p L $ \alpha_{p}^{L} $ and β p L $ \beta_{p}^{L} $ with some interesting arithmetic properties. For instance, β p L $ \beta_{p}^{L} $ is equal to 1 whenever p does not ramify in L and α p L $ \alpha_{p}^{L} $ is divisible by p whenever p is wildly ramified in L. The aforementioned properties, although interesting, follow easily from definitions; however a more interesting application of these invariants is the fact that they completely characterize the Dedekind zeta function of L. Moreover, if the residue class mod p of α p L $ \alpha_{p}^{L} $ is not zero for all p then such residues determine the genus of the integral trace.
2012 ◽
Vol 08
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pp. 125-147
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2015 ◽
Vol 93
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pp. 199-210
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2007 ◽
Vol 03
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pp. 217-229
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2013 ◽
Vol 12
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pp. 137-165
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2003 ◽
Vol 31
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pp. 23-92
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1995 ◽
Vol 138
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pp. 199-208
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