Factorization of zeta-functions, reciprocity laws, non-vanishing
نویسنده
چکیده
The factorization of ζo(s) is the main issue. After giving a definition of this zeta function, we will see that the factorization is equivalent to understanding the behavior of rational primes in the extension ring Z[ω] of Z: do they stay prime, or do they factor as products of primes in Z[ω]? A complication is that the rings Z[ω] are rarely principal ideal domains. To delay contemplation of this, we treat several examples of factorization where the rings involved are principal ideal domains.
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