Hey, Im looking for an example of a Dirichlet series , whose convergence abscissa differs from its absolute convergence abcissa, but the difference is strictly less than 1.

Can you help me, and is it clear what Im looking for?

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- Apr 28th 2011, 06:21 AMEinStoneDirichlet Series Example
Hey, Im looking for an example of a Dirichlet series , whose convergence abscissa differs from its absolute convergence abcissa, but the difference is strictly less than 1.

Can you help me, and is it clear what Im looking for? - Apr 28th 2011, 08:24 AMFernandoRevilla
- Apr 28th 2011, 08:26 AMEinStone
There is no complex variable in your series.

- Apr 28th 2011, 08:34 AMFernandoRevilla
- Apr 28th 2011, 08:46 AMEinStone
I meant an example with an arbitrary complex s, for instance converges for Re s > 0 and converges absolutely for Re s > 1. SO the difference of the abscissa is exactly 1. I am now looking for an example where the difference is strictly between 0 and 1.