3 ms·

I need a “Explain like I’m 5” for Landau--Siegel zeros. This sounds like a hard task as I couldn’t find anything online that does it :(

• gavagai691 4y ago
  Hey, this comment was my attempt at an ELIUndergraduate (5 is probably a little too ambitious for this topic). I hope it may be helpful! https://old.reddit.com/r/math/comments/y93a86/eliundergraduate_the_hype_around_yitang_zhangs/it4kdrn/ https://old.reddit.com/r/math/comments/y93a86/eliundergradua...
  • 3a2d29 4y ago
    Thanks!
• leokennis 4y ago
  There are moments I'm pretty proud of my intellect and what I have achieved with it. Reading and not comprehending even the very basics of proofs like Zhang's are a good reality check in that regard.
• dudeinjapan 4y ago
  There is a function called the Riemann Zeta function which is defined as an infinite series ZETA(s) = 1/1^s + 1/2^s + 1/3^s + ... For certain complex number inputs s, this function ZETA(s) returns zero. Riemann's hypothesis states it returns zero when the real part of the input Re(s) = 1/2, and the imaginary part Im(s) some non-zero value (the first zero occurs at Im(s) = +/- 14.135.) As far as we've checked with computers, all zeroes have Re(s) = 1/2. We are interested in these "zeros" because we can use them to construct a harmonic function (think overlapping waves) which tells us how the prime numbers are distributed. A Siegel zero is a potential counterexample where a zero could theoretically occur for complex number with Re(s) close to 1 (i.e. not 1/2.) This is based on the study of Dirichlet-L functions which are a generalized version (i.e. superset) of the Riemann Zeta function. If Zhang's result is correct, it simplifies the problem space for finding Riemann zeros, and thus for understanding the distribution of primes.