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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”)
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4
awarded  Yearling
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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
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4
awarded  Yearling
Oct
5
awarded  Popular Question
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28
awarded  Popular Question