fields, the problem is essentially a planar lattice point problem (cf. ZAGIER [17]). To this, the deep results of HUXLEY [3], [4] can be applied to get For cubic fields, W. MULLER [12] proved that ## 43 - (h the class number), using a deep exponential sum technique due to KOLESNIK [7]. every n
On the distribution of ideals in cubic number fields
✍ Scribed by Wolfgang Müller
- Publisher
- Springer Vienna
- Year
- 1988
- Tongue
- English
- Weight
- 323 KB
- Volume
- 106
- Category
- Article
- ISSN
- 0026-9255
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📜 SIMILAR VOLUMES
For y # R >0 an integral ideal of an algebraic number field F is called y-smooth if the norms of all of its prime ideal factors are bounded by y. Assuming the generalized Riemann hypothesis we prove a lower bound for the number F (x, y) of integral y-smooth ideals in F whose norms are bounded by x #
In this paper it is shown that the sum of class numbers of orders in complex cubic fields obeys an asymptotic law similar to the prime numbers as the bound on the regulators tends to infinity. Here only orders are considered which are maximal at two given primes. This result extends work of Sarnak i