What are trivial zeroes?

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The Reimann Hypothesis is an interesting topic to me, but as a high school student, I can’t seem to find an understandable definition of a trivial zero. How could an infinite sum result in nothing?

In: Mathematics

3 Answers

Anonymous 0 Comments

“trivial”=”boring/obvious”, so this is not a special type of zero, but just the ones we don’t care about.

The Riemann hypothesis than simply reads “all other zeros than that have real part 1/2”.

> How could an infinite sum result in nothing?

Take an infinite sum that results in something, e.g. 1+1/2+1/4+ … =2.
Subtract that from the first term to get -1+1/2+1/4+…=0.

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