Siegel zero

A Siegel zero is a hypothetical, very close-to-1 zero of a certain mathematical function called an L-function, related to prime numbers in arithmetic progressions. Its existence was once suspected but remains unproven. If such a zero exists, it would imply some irregularities in how primes are distributed, especially among certain residue classes. Mathematicians generally believe Siegel zeros do not exist, and their absence supports the regularity of the distribution of prime numbers. The concept is important in understanding deep aspects of number theory and the behavior of primes within different numerical systems.