#Riemann zeta function

21 messages · Page 1 of 1 (latest)

blissful tinselBOT
solar elbow
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why would it be infinite?

inland apex
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An infinite sum of n² is just infinite, no?

solar elbow
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proof?

inland apex
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Well 1+4+9+16 doesn't seem to be leading to zero either way

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I'm tryna figure why it's a trivial zero, not why it's not infinite

solar elbow
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hold up misread ur q

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oh right

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so for negative s this definition isnt the right one

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mathematicians care about its analytic continuation for Re(s)<=1

inland apex
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Negative even integers are said to be the trivial zeros tho

solar elbow
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not of the infinite sum

inland apex
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Ok, but what's the continuation calculated by?

solar elbow
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https://en.wikipedia.org/wiki/Analytic_continuation

Analytic continuation

In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function. Analytic continuation often succeeds in defining further values of a function, for example in a new region where the infinite series representation which initially defined the function becomes diverg...

inland apex
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What's the continuation of the Riemann function, I mean

solar elbow
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https://en.wikipedia.org/wiki/Analytic_continuation#Example_I:_The_connection_of_the_Riemann_zeta_function_to_the_Bernoulli_numbers

Analytic continuation

In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function. Analytic continuation often succeeds in defining further values of a function, for example in a new region where the infinite series representation which initially defined the function becomes diverg...

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its not simple

inland apex
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Oh bruh I didn't see that yet

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Alr well that's enough for moi

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Thanks