@article{ZNSL_2023_523_a9,
author = {A. L. Smirnov},
title = {On {Gauss'} rings and {Deuring's} argument},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {159--165},
year = {2023},
volume = {523},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_523_a9/}
}
A. L. Smirnov. On Gauss' rings and Deuring's argument. Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 6, Tome 523 (2023), pp. 159-165. http://geodesic.mathdoc.fr/item/ZNSL_2023_523_a9/
[1] A. L. Smirnov, “O slozheniyakh na multiplikativnom monoide tselykh chisel”, Zap. nauchn. semin. POMI, 502, 2021, 139–151
[2] N. Durov, New Approach to Arakelov Geometry, 16 Apr 2007, arXiv: 0704.2030v1 [math AG]
[3] D. Goldfeld, “Gauss' class number problem for imaginary quadratic fields”, Bull. of AMS, 13:1, July (1985) | DOI | MR | Zbl
[4] I. R. Shafarevich, “Problema desyatogo diskriminanta”, Algebra i analiz, 25:4 (2013), 260–277
[5] R. E. MacRae, “On Unique Factorization in Certain Rings of Algebraic Functions”, J. of Algebra, 17 (1971), 243–261 | DOI | MR | Zbl
[6] M. L. Madan, C. S. Queen, “Algebraic Function Fields of class number one”, Acta Arithmetica, XX (1972), 424–431 | MR
[7] J. R. C. Leitzel, M. L. Madan, C. S. Queen, “Algebraic Function Fields with Small Class Number”, J. Number Theory, 7 (1975), 11–27 | DOI | MR | Zbl
[8] C. Stirpe, “A counterexample to ‘Algebraic function fields with small class number’”, J. Number Theory, 143 (2014), 402–404 | DOI | MR | Zbl
[9] P. Mercuri, C. Stirpe, Classification of algebraic function fields with class number one, 2014, arXiv: 1406.5365v3 | MR
[10] Q. Shen, S. Shi, “Function fields of class number one”, NY Number Theory Conference, 2015 | MR
[11] M. Deuring, “Imaginare quadratische Zahlkörper mit der Klassenzahl 1”, Math. Z., 37 (1933), 405–415 | DOI | MR | Zbl
[12] E. Landau, “Über die Klassenzahl imaginär-quadratische Zahlkörper”, Gött. Nachr, 1918, 285–295