Theory and Modern Applications
Table 1 Numerical values of \(\mathcal{O}_{1}\) and \(\Lambda _{1}\) for \(\in [1.1,2.6]\) in Example 6.1 when \(\mathbb{G}_{1}=2^{\mathfrak{t}}\)
t | \(\mathcal{O}_{1}\) | \(L\mathcal{O}_{1}<1\) | \(\mathcal{O}_{1}\) | \(\ell _{1} \geq \) |
|---|---|---|---|---|
1.10 | 0.000000 | 0.000000 | 11.770000 | 11.770000 |
1.20 | 0.441466 | 0.014716 | 16.049142 | 16.427116 |
1.30 | 0.823549 | 0.027452 | 19.031261 | 19.829775 |
1.40 | 1.316793 | 0.043893 | 22.196803 | 23.640848 |
1.50 | 1.949409 | 0.064980 | 25.691224 | 28.120080 |
1.60 | 2.747700 | 0.091590 | 29.597402 | 33.515007 |
1.70 | 3.740314 | 0.124677 | 33.984940 | 40.144312 |
1.80 | 4.959615 | 0.165320 | 38.922357 | 48.465235 |
1.90 | 6.442580 | 0.214753 | 44.481788 | 59.178840 |
2.00 | 8.231606 | 0.274387 | 50.741485 | 73.430081 |
2.10 | 10.375358 | 0.345845 | 57.787565 | 93.234045 |
2.20 | 12.929718 | 0.430991 | 65.715482 | 122.503611 |
2.30 | 15.958843 | 0.531961 | 74.631461 | 169.978522 |
2.40 | 19.536380 | 0.651213 | 84.653973 | 259.995318 |
2.50 | 23.746839 | 0.791561 | 95.915326 | 495.319774 |