2015 Fiscal Year Final Research Report
Second main terms for density theorems in number theory
Project/Area Number |
24654005
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Research Category |
Grant-in-Aid for Challenging Exploratory Research
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Allocation Type | Multi-year Fund |
Research Field |
Algebra
|
Research Institution | Kobe University |
Principal Investigator |
Taniguchi Takashi 神戸大学, 理学(系)研究科(研究院), 准教授 (60422391)
|
Project Period (FY) |
2012-04-01 – 2016-03-31
|
Keywords | 第二主要項 / 密度定理 / 三次体 / 概均質ベクトル空間 / 指数和 |
Outline of Final Research Achievements |
We studied in details the second main terms in counting discriminants of certain families of number fields. The results include: On the counting function for non-commutative sextic Galois fields, we get an evidence that there might exist the tertiary main term. On the counting function for relative cubic extensions, when the base field is a quadratic field, we determined the second main term; over a general number field, we determined the second main term for a smoothed counting function. We have several more results. As a related problem, we discover a simple method to evaluate certain exponential sums associated with prehomogeneous vector spaces.
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Free Research Field |
整数論
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