On Iwasawa lambda3-invariants of cyclic cubic fields of prime conductor
نویسندگان
چکیده
For certain cyclic cubic fields k, we verified that Iwasawa invariants λ3(k) vanished by calculating units of abelian number field of degree 27. Our method is based on the explicit representation of a system of cyclotomic units of those fields.
منابع مشابه
On Iwasawa Λ3-invariants of Cyclic Cubic Fields of Prime Conductor
For certain cyclic cubic fields k, we verified that Iwasawa invariants λ3(k) vanished by calculating units of abelian number field of degree 27. Our method is based on the explicit representation of a system of cyclotomic units of those fields.
متن کاملA Lower Bound for the Class Number of Certain Cubic Number Fields
Let AT be a cyclic number field with generating polynomial i a— 3 ^ û + 3 x3 —Y-x1 -=~-xi and conductor m. We will derive a lower bound for the class number of these fields and list all such fields with prime conductor m = (a1 + 21)/A or m = (1 + 21b2)/A and small class number.
متن کاملComputation of Iwasawa ν-invariants of certain real abelian fields
Let p be a prime number and k a finite extension of Q. It is conjectured that Iwasawa invariants λp(k) and μp(k) vanish for all p and totally real number fields k. Using cyclotomic units and Gauss sums, we give an effective method for computing the other Iwasawa invariants νp(k) of certain real abelian fields. As numerical examples, we compute Iwasawa invariants associated to k = Q( √ f, ζp + ζ...
متن کاملCyclotomy and Delta Units
In this paper we examine cyclic cubic, quartic, and quintic number fields of prime conductor p containing units that bear a special relationship to the classical Gaussian periods: n¡ nj+x + c is a unit for periods r\¡ and c e Z.
متن کامل2 2 N ov 2 00 4 Iwasawa Theory of Elliptic Curves at Supersingular Primes over Z p - extensions of Number Fields
In this paper, we make a study of the Iwasawa theory of an elliptic curve at a supersingular prime p along an arbitrary Zp-extension of a number field K in the case when p splits completely in K. Generalizing work of Kobayashi [8] and Perrin-Riou [16], we define restricted Selmer groups and λ ± , µ ±-invariants; we then derive asymptotic formulas describing the growth of the Selmer group in ter...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Math. Comput.
دوره 70 شماره
صفحات -
تاریخ انتشار 2001