A simple proof of η(— 1/τ)= η(τ)√τ/i

Carl Ludwig Siegel

doi:10.1112/S0025579300000462

Extract

This functional equation for Dedekind's

has been established in many different ways; however, it seems that the following proof, a straightforward application of the theorem of residues, has not been observed before. Since

it suffices to prove that

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A simple proof of η(— 1/τ)= η(τ)√τ/i

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