Abstract.
The primary concern of this paper is to present three further applications of a multi-dimensional version of Bombieri’s theorem on primes in arithmetic progressions in the setting of a totally real algebraic number field K. First, we deal with the order of magnitude of a greatest (relative to its norm) prime ideal factor of , where the product runs over prime arguments ω of a given irreducible polynomial F which lie in a certain lattice point region. Then, we turn our attention to the problem about the occurrence of algebraic primes in a polynomial sequence generated by an irreducible polynomial of K with prime arguments. Finally, we give further contributions to the binary Goldbach problem in K.
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(Received 11 January 2000; in revised form 4 December 2000)
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Hinz, J. Some Applications of a Bombieri-Type Theoremin Totally Real Number Fields. Mh Math 132, 105–121 (2001). https://doi.org/10.1007/s006050170048
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DOI: https://doi.org/10.1007/s006050170048