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TWO PROBLEMS CONCERNING IRREDUCIBLE ELEMENTS IN RINGS OF INTEGERS OF NUMBER FIELDS
| Content Provider | Scilit |
|---|---|
| Author | Pollack, Paul Troupe, Lee |
| Copyright Year | 2017 |
| Description | Let $K$ be a number field with ring of integers $\mathbb{Z}_{K}$ . We prove two asymptotic formulas connected with the distribution of irreducible elements in $\mathbb{Z}_{K}$ . First, we estimate the maximum number of nonassociated irreducibles dividing a nonzero element of $\mathbb{Z}_{K}$ of norm not exceeding $x$ (in absolute value), as $x\rightarrow \infty$ . Second, we count the number of irreducible elements of $\mathbb{Z}_{K}$ of norm not exceeding $x$ lying in a given arithmetic progression (again, as $x\rightarrow \infty$ ). When $K=\mathbb{Q}$ , both results are classical; a new feature in the general case is the influence of combinatorial properties of the class group of $K$ . |
| Related Links | http://arxiv.org/pdf/1610.08410 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/DCE43D12573DE107CAC946F0CCE93F5F/S0004972716001325a.pdf/div-class-title-two-problems-concerning-irreducible-elements-in-rings-of-integers-of-number-fields-div.pdf |
| Ending Page | 58 |
| Page Count | 15 |
| Starting Page | 44 |
| ISSN | 00049727 |
| e-ISSN | 17551633 |
| DOI | 10.1017/s0004972716001325 |
| Journal | Bulletin of the Australian Mathematical Society |
| Issue Number | 1 |
| Volume Number | 96 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2017-08-01 |
| Access Restriction | Open |
| Subject Keyword | Bulletin of the Australian Mathematical Society Mathematical Physics Davenport Constant |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
