the number google has 110 zeros.
how many zeros does the number google have?
110
Na
Na
fortunately other methods were pioneered in the nineteenth century to deal with the algebraic properties of "e", and consequently of π through euler's identity. this work centred on use of the so-called auxiliary function. these are functions which typically have many zeros at the points under consideration. here "many zeros" may mean many distinct zeros, or as few as one zero but with a high multiplicity, or even many zeros all with high multiplicity. charles hermite used auxiliary functions that approximated the functions "e" for each natural number "k" in order to prove the transcendence of "e" in 1873. his work was built upon by ferdinand von lindemann in the 1880s in order to prove that "e" is transcendental for nonzero algebraic numbers α. in particular this proved that π is transcendental since "e" is algebraic, and thus answered in the negative the problem of antiquity as to whether it was possible to square the circle. karl weierstrass developed their work yet further and eventually proved the lindemann–weierstrass theorem in 1885.
transcendental number theory