Timeline for Examples of nice families of irreducible polynomials over Z
Current License: CC BY-SA 2.5
3 events
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| Nov 9, 2010 at 18:10 | comment | added | trew | It might be useful for me to have a polynomial not in the explicit form where you can use perron,but like polynomials in the examples,also it is a problem to have a very big coefficient,if you need to "kill" for example a term like the sum of the a_k to get a easier form mod p^k(see my first example: its usefull to elimate the sum of the a_k ) | |
| Nov 9, 2010 at 18:03 | comment | added | trew | hi,thank you!I know Perron.Eistenstein is not very useful because then the derivation modulo p is a bit boring,there should be cases where its 0 and not 0 for different x.I look at polynomials and their zeros modulo p^k and i have lemmas involving the derivation to tell me how the "lifting" of the zeros to a zero mod p^(k+1) might look like and how many there are.Its hard to tell in a short way and i know no book about it,just a short text in german. | |
| Nov 9, 2010 at 17:54 | history | answered | Qiaochu Yuan | CC BY-SA 2.5 |