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In this abridged version of [Lou], we outline an efficient technique for computing relative class numbers of imaginary abelian fields. It enables us to compute relative class numbers of imaginary cyclic fields of degrees 32 and conductors greater than 1013, or of degrees 4 and conductors greater than 1015. Our major innovation is a technique for computing numerically root numbers appearing in some...
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Mathematische Nachrichten > 284 > 5‐6 > 608 - 628
In this paper, we prove the weak p‐part of the Tamagawa number conjecture in all non‐critical cases for the motives associated to Hecke characters of the form where φ is the Hecke character of a CM elliptic curve E defined over an imaginary quadratic field K, under certain restrictions which originate mainly from the Iwasawa theory of imaginary quadratic fields. © 2011...
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manuscripta mathematica > 2001 > 106 > 4 > 411-427
Abstract: Let \lcub;Km}m 4 be the family of non-normal totally real cubic number fields associated with the Q-irreducible cubic polynomials Pm(x) =x3mx2(m+1)x 1, m 4. We determine all these Kms with class numbers hm 3: there are 14 such Kms. Assuming the Generalized Riemann hypothesis for all the real quadratic number fields, we also prove that the exponents em of the ideal class groups of these Km...
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Mathematische Zeitschrift > 2000 > 233 > 2 > 251-263
Abstract. We explicitly calculate all the 2-primary higher algebraic K-groups of the rings of integers of all 2-regular quadratic number fields, cyclotomic number fields, or maximal real subfields of such. Here 2-regular means that (2) does not split in the number field, and its narrow Picard group is of odd order.
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