Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

in the paper http://www.fuchs-braun.com/media/dd209bf5c2203a87ffff80a3ffffffef.pdf section 2 ' Hilbert-Polya space' page: 180 the author introduce the Theta series

$$ F(\phi(x))= x^{1/2}\sum_{n=0}^{\infty}\phi (nx) $$ x >0

of course if we take the Mellin transform of this we will get the formula

$$ G(1/2+is)\zeta(1/2+is) $$

$$ G(s)= \int_{0}^{\infty}dtF(\phi(t))t^{s-1} $$

then the author affirms that the function vanishes at the Riemann zeros only

i know all the properties of this function but why does the authoer introduce it ?? he wants to give an spectral interpretation but how does the spectral interpretation appears from this series ??

share|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.