caa a22 4500 467989427 CHVBK 20180323112540.0 cr unu---uuuuu 170328e19900901xx s 000 0 eng 10.1007/BF01301678 doi (NATIONALLICENCE)springer-10.1007/BF01301678 Girstmair Kurt Institut für Mathematik, Universität Innsbruck, Technikerstrasse 25, A-6020, Innsbruck, Austria aut Dirichlet convolution of cotangent numbers and relative class number formulas [Elektronische Daten] [Kurt Girstmair] Letn be the conductor of an abelian number fieldK. The numbersicot (πk/n), (k, n)=1, belong to, then-th cyclotomic field; theirK-traces form an additive group whose index in the "imaginary part” of the ringO K involves the relative class numberh K − ofK. This was shown previously. In the present paperh K − is decomposed into "branch factors”, each of which is shown to be the index of an additive group of modified cotangent numbers. Put together in the right way, the said numbers yield formulas forh K − simpler than the previous ones. The different types of cotangent numbers are mutually connected by Dirichlet convolution, whose meaning in the construction of cyclotomic numbers is studied. Finally, our results are rephrased in terms of Stickelberger ideals. Springer-Verlag, 1990 Monatshefte für Mathematik Springer-Verlag 110/3-4(1990-09-01), 231-256 0026-9255 110:3-4<231 1990 110 605 https://doi.org/10.1007/BF01301678 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01301678 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Girstmair Kurt Institut für Mathematik, Universität Innsbruck, Technikerstrasse 25, A-6020, Innsbruck, Austria aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer-Verlag 110/3-4(1990-09-01), 231-256 0026-9255 110:3-4<231 1990 110 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer