View Proposal #137
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| ID | 137 |
|---|---|
| First Name | Christian |
| Last Name | Roettger |
| Institution | Iowa State University |
| Speaker Category | faculty |
| Title of Talk | Prime divisors of Mersenne numbers and Dirichlet series |
| Abstract | Mersenne numbers are the numbers 1, 3, 7, 15, ... 2^n - 1, ... It is a long-standing conjecture that this sequence contains infinitely many primes. We show how to get some asymptotic results on the 'average' prime divisor of Mersenne numbers using Dirichlet series. These series are useful for asymptotic counting, because there is a close link between their domain of convergence and the growth of their coefficients. Do not expect a big breakthrough, but a pretty result, few technicalities, and some exciting open questions. |
| Subject area(s) | Number Theory |
| Suitable for undergraduates? | Yes |
| Day Preference | |
| Computer Needed? | N |
| Bringing a laptop? | Y |
| Overhead Needed? | N |
| Software requests | |
| Special Needs | Would like projector to use with own laptop - can use overhead as fallback. |
| Date Submitted | 3/16/2005 |
| Year | 2005 |