Remarks on number theory over additive arithmetical semigroups

• Date: 2020
• Main Authors: Indlekofer, K.-H., Kaya, E.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2020
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/6042
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 511 We deal with additive arithmetical semigroups and present old and new proofs for the distribution of zeros of the corresponding $\zeta$-functions.  We use these results to prove prime number theorems and a Selberg formula for such semigroups.