TY - JOUR AU - K.-H. Indlekofer AU - E. Kaya PY - 2020/03/28 Y2 - 2024/03/29 TI - Remarks on number theory over additive arithmetical semigroups JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 72 IS - 3 SE - Research articles DO - 10.37863/umzh.v72i3.6042 UR - https://umj.imath.kiev.ua/index.php/umj/article/view/6042 AB - UDC 511We 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. ER -