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May
1 |
awarded | Popular Question |
Jul
2 |
awarded | Curious |
May
19 |
accepted | Isomorphism classes of nilpotent Lie algebras |
Jul
23 |
accepted | Convergence of Dirichlet series (“at the boundary”) |
Jul
23 |
comment |
Convergence of Dirichlet series (“at the boundary”)
@GH: OK, sorry to bother you one more time, but I wonder if you know whether the theorem from Newman you mentioned is true if instead of assuming that $|a_n|$ is bounded, one merely assumed that $|a_n|=o(n^\epsilon)$ for any $\epsilon>0$? I've looked at the proof, and it seems like I $might$ be able to generalize it to this case, but I could be making a mistake, and if you know the answer off the top of your head, I would really appreciate it. |
Jul
22 |
comment |
Convergence of Dirichlet series (“at the boundary”)
@Kevin: not really, because I am not making any monotonicity assumptions. For example, the $a_n$ with even $n$ could go to zero very slowly, and the $a_n$ with odd $n$ could go to zero very quickly; then the series would not converge for $s=1$. |
Jul
22 |
comment |
Convergence of Dirichlet series (“at the boundary”)
Thanks! Unfortunately, the assumptions of the theorem from Newman that you mentioned are too strong for me. In the situations I am interested in, the numbers $a_n$ are all real, their signs alternate, $|a_n|$ doesn't grow too quickly (slower than $n^\epsilon$ for any $\epsilon>0$), and $s_0=1$. I wonder if you have any insight into this particular case? |
Jul
22 |
asked | Convergence of Dirichlet series (“at the boundary”) |
Mar
4 |
awarded | Yearling |
Feb
23 |
awarded | Notable Question |
Oct
15 |
awarded | Nice Question |
Oct
15 |
comment |
Motivation behind the construction of Deligne and Lusztig
Thank you for the explanations! (Also, I corrected the spelling of Macdonald's name.) |
Oct
15 |
accepted | Motivation behind the construction of Deligne and Lusztig |
Oct
15 |
revised |
Motivation behind the construction of Deligne and Lusztig
edited body |
Oct
12 |
comment |
Motivation behind the construction of Deligne and Lusztig
This is true, although the D-L varieties corresponding to usual H-C induction are finite sets, which makes the leap even bigger, in some sense! I am in no way trying to downplay the genius of Deligne and Lusztig; however, there are many other very remarkable constructions in mathematics that do have intuitive explanations behind them. For a related example, look at Lusztig's theory of character sheaves: their definition is also not at all obvious, but it was motivated by a huge amount of concrete calculations, unlike the Deligne-Lusztig theory, which appears to have grown out of one example. |
Oct
12 |
asked | Motivation behind the construction of Deligne and Lusztig |
Jun
29 |
accepted | Interchanging min and max for a continuous function of two variables |
Jun
27 |
asked | Interchanging min and max for a continuous function of two variables |
Mar
4 |
awarded | Yearling |
Oct
5 |
awarded | Popular Question |