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Let p be a prime number. For a number field k, let k be the compositum of all ℤp-extensions of k. Then Greenberg’s generalized conjecture (GGC) claims that the unramified… Click to show full abstract
Let p be a prime number. For a number field k, let k be the compositum of all ℤp-extensions of k. Then Greenberg’s generalized conjecture (GGC) claims that the unramified Iwasawa module X(k) is pseudo-null over the Iwasawa algebra associated to the Galois group of k/k. In this paper, we establish sufficient conditions of GGC when k is a complex cubic field and give many examples which satisfy the conditions with the help of computer programs.
Keywords:
conjecture complex;
greenberg generalized;
generalized conjecture;
complex cubic;
cubic fields
Journal Title: International Journal of Number Theory
Year Published: 2017
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Journal Title: International Journal of Number Theory
Year Published: 2017
Link to full text (if available)
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recommendations!