# number of zeros of complex waves

Does anybody know about any type of methods how to calucalte/estimate the number of the zeros of complex waves (periodic functions as superposition of many harmonic waves) within a given period [0,x] under the condition that the wave function is even? - It is indeed about the number of zeros and not determining the zeros themselves.

Does anybody knows about problems rising in other disciplines like physiscs where the number of such zeros are studied and essential?

Alternatively, if there might be a proof that such method can not generally exist (for instance because of a type of uncertainty principle), it would be also very helpful.

Many thanks

• encyclopediaofmath.org/index.php/Rouch%C3%A9_theorem Commented Mar 27, 2013 at 6:08
• see: [partly dealt in another post][1] [1]: math.stackexchange.com/questions/377997/… Commented May 25, 2013 at 9:26
• Perhaps you would find Riemann-Roch useful? en.wikipedia.org/wiki/Riemann%E2%80%93Roch_theorem
– Neal
Commented Nov 14, 2014 at 17:07
• why/how Rieman-Roch? may you explain more details please? Commented Nov 14, 2014 at 17:48
• I will just say that this is equivalent to asking: "without calculating any eigenvalues, how many distinct eigenvalues does this matrix have?" The question here shows this: math.stackexchange.com/questions/370996/… Without more about the nature of the series coefficients, I don't think it is possible to to count eigenvalues/roots without calculating them first. Commented Nov 21, 2014 at 19:08