Halter-Koch, Franz Class field theory and \(L\) functions. Foundations and main results. (English) Zbl 1506.11001 Boca Raton, FL: CRC Press (ISBN 978-1-138-58358-0/hbk; 978-1-032-20265-5/pbk; 978-0-429-50657-4/ebook). xix, 564 p. (2022). Reviewer: Robert W. van der Waall (Huizen) MSC: 11-01 11Mxx 11Rxx PDFBibTeX XMLCite \textit{F. Halter-Koch}, Class field theory and \(L\) functions. Foundations and main results. Boca Raton, FL: CRC Press (2022; Zbl 1506.11001) Full Text: DOI
Schempp, Walter J. Congruence and metaplectic covariance: rational biquadratic reciprocity and quantum entanglement. (English) Zbl 1488.11171 Constr. Math. Anal. 4, No. 1, 61-80 (2021). MSC: 11R37 81P40 PDFBibTeX XMLCite \textit{W. J. Schempp}, Constr. Math. Anal. 4, No. 1, 61--80 (2021; Zbl 1488.11171) Full Text: DOI
Gorchinskiy, S. O. Orthogonal to principal ideles. (English) Zbl 1451.11122 Math. Notes 107, No. 3, 425-434 (2020). MSC: 11R37 11R56 14H05 11G20 PDFBibTeX XMLCite \textit{S. O. Gorchinskiy}, Math. Notes 107, No. 3, 425--434 (2020; Zbl 1451.11122) Full Text: DOI arXiv
Hughes, Adam M. A Weil Banach algebra for multiplicative algebraic numbers. (English) Zbl 1454.11207 J. Number Theory 196, 244-271 (2019). MSC: 11R56 11R04 PDFBibTeX XMLCite \textit{A. M. Hughes}, J. Number Theory 196, 244--271 (2019; Zbl 1454.11207) Full Text: DOI
Applebaum, David Probabilistic trace and Poisson summation formulae on locally compact abelian groups. (English) Zbl 1360.60011 Forum Math. 29, No. 3, 501-517 (2017); corrigendum ibid. 29, No. 6, 1499-1500 (2017). MSC: 60B15 60E07 11F85 43A25 11R56 PDFBibTeX XMLCite \textit{D. Applebaum}, Forum Math. 29, No. 3, 501--517 (2017; Zbl 1360.60011) Full Text: DOI arXiv Link
Dumbaugh, Della; Schwermer, Joachim [Cogdell, James; Langlands, Robert] Emil Artin and beyond. Class field theory and \(L\)-functions. With contributions by James Cogdell and Robert Langlands. (English) Zbl 1321.11002 Heritage of European Mathematics. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-146-0/hbk). xiii, 231 p. (2015). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11-03 11-02 11R37 11R39 11F66 11F67 11M06 01A60 01A70 PDFBibTeX XMLCite \textit{D. Dumbaugh} and \textit{J. Schwermer}, Emil Artin and beyond. Class field theory and \(L\)-functions. With contributions by James Cogdell and Robert Langlands. Zürich: European Mathematical Society (EMS) (2015; Zbl 1321.11002) Full Text: DOI
Braunling, Oliver Geometric two-dimensional idèles with cycle module coefficients. (English) Zbl 1319.11082 Math. Nachr. 287, No. 17-18, 1954-1971 (2014). Reviewer: Valeriu Popa (Chişinău) MSC: 11R56 11G45 PDFBibTeX XMLCite \textit{O. Braunling}, Math. Nachr. 287, No. 17--18, 1954--1971 (2014; Zbl 1319.11082) Full Text: DOI arXiv
Childress, Nancy Class field theory. (English) Zbl 1165.11001 Universitext. New York, NY: Springer (ISBN 978-0-387-72489-8/pbk). x, 226 p. (2009). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11-01 11R37 PDFBibTeX XMLCite \textit{N. Childress}, Class field theory. New York, NY: Springer (2009; Zbl 1165.11001) Full Text: DOI
Knapp, Anthony W. Advanced algebra. Along with a companion volume ‘Basic algebra’. (English) Zbl 1133.00001 Cornerstones. Basel: Birkhäuser (ISBN 978-0-8176-4522-9/hbk; 978-0-8176-4533-5/set). xxiv, 730 p. (2007). Reviewer: Werner Kleinert (Berlin) MSC: 00A05 11-01 14-01 16-01 18-01 12-01 PDFBibTeX XMLCite \textit{A. W. Knapp}, Advanced algebra. Along with a companion volume `Basic algebra'. Basel: Birkhäuser (2007; Zbl 1133.00001) Full Text: DOI
Iyanaga, Shōkichi The works of Claude Chevalley on class field theory: an introduction. (Travaux de Claude Chevalley sur la théorie du corps de classes: introduction.) (French) Zbl 1172.11041 Jpn. J. Math. (3) 1, No. 1, 25-85 (2006). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R37 11-03 01A60 01A70 PDFBibTeX XMLCite \textit{S. Iyanaga}, Jpn. J. Math. (3) 1, No. 1, 25--85 (2006; Zbl 1172.11041) Full Text: DOI
Cohen, Paula B. Noncommutative number theory. (English) Zbl 1102.11042 Nathanson, Melvyn B. (ed.), Unusual applications of number theory. Proceedings of the DIMACS workshop held at Rutgers University, Piscataway, NJ, USA, January 10–14, 2000. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-2703-0/hbk). DIMACS. Series in Discrete Mathematics and Theoretical Computer Science 64, 37-51 (2004). Reviewer: Samuel James Patterson (Göttingen) MSC: 11M06 11R56 46L89 PDFBibTeX XMLCite \textit{P. B. Cohen}, DIMACS, Ser. Discrete Math. Theor. Comput. Sci. 64, 37--51 (2004; Zbl 1102.11042)
Gras, Georges Class field theory. From theory to practice. (English) Zbl 1019.11032 Springer Monographs in Mathematics. Berlin: Springer. xiii, 491 p. EUR 79.95/net; sFr 133.00; £56.00; $ 79.95 (2003). Reviewer: Wladyslaw Narkiewicz (Wrocław) MSC: 11R37 11-01 11-02 11R29 11R20 11S31 PDFBibTeX XMLCite \textit{G. Gras}, Class field theory. From theory to practice. Berlin: Springer (2003; Zbl 1019.11032)
Connes, Alain Trace formula in noncommutative geometry and the zeros of the Riemann zeta function. (English) Zbl 0945.11015 Sel. Math., New Ser. 5, No. 1, 29-106 (1999). Reviewer: Audrey A. Terras (La Jolla) MSC: 11M55 11M26 11R56 11F72 58J50 58J90 PDFBibTeX XMLCite \textit{A. Connes}, Sel. Math., New Ser. 5, No. 1, 29--106 (1999; Zbl 0945.11015) Full Text: DOI arXiv Numdam
Jaulent, Jean-François Global \(\ell\)-adique clean field theory. (Théorie \(\ell\)-adique globale du corps de classes.) (French) Zbl 0938.11052 J. Théor. Nombres Bordx. 10, No. 2, 355-397 (1998). Reviewer: C.Parry (Blacksburg) MSC: 11R37 11R56 11S37 PDFBibTeX XMLCite \textit{J.-F. Jaulent}, J. Théor. Nombres Bordx. 10, No. 2, 355--397 (1998; Zbl 0938.11052) Full Text: DOI Numdam EuDML EMIS
Koch, Helmut Number theory: algebraic numbers and functions. (Zahlentheorie: algebraische Zahlen und Funktionen.) (German) Zbl 0885.11001 Vieweg Studium: Aufbaukurs Mathematik. 72. Wiesbaden: Vieweg. xii, 344 S. (1997). Reviewer: V.Ennola (Turku) MSC: 11-01 11Rxx 11Axx 11R11 11R04 11R42 11R44 11R27 11R29 11R37 11A55 PDFBibTeX XMLCite \textit{H. Koch}, Zahlentheorie: algebraische Zahlen und Funktionen. Wiesbaden: Vieweg (1997; Zbl 0885.11001)
Burns, D. On twisted Galois-Gauß sums and canonical factorizations. (English) Zbl 0823.11067 Math. Z. 218, No. 2, 159-178 (1995). Reviewer: J.Brinkhuis (Rotterdam) MSC: 11R33 PDFBibTeX XMLCite \textit{D. Burns}, Math. Z. 218, No. 2, 159--178 (1995; Zbl 0823.11067) Full Text: DOI EuDML
Lang, Serge Algebraic number theory. 2nd ed. (English) Zbl 0811.11001 Graduate Texts in Mathematics. 110. New York: Springer-Verlag. xiii, 357 p. (1994). Reviewer: M.Sheingorn (New York) MSC: 11-02 11-01 11Rxx 11Sxx PDFBibTeX XMLCite \textit{S. Lang}, Algebraic number theory. 2nd ed. New York: Springer-Verlag (1994; Zbl 0811.11001)
Vladimirov, V. S. Freund-Witten adelic formulae for Veneziano and Virasoro-Shapiro amplitudes. (English. Russian original) Zbl 0866.11068 Russ. Math. Surv. 48, No. 6, 1-39 (1993); translation from Usp. Mat. Nauk 48, No. 6(294), 3-38 (1993). Reviewer: W.Wiȩsław (Wrocław) MSC: 11S80 46S10 81T30 11S31 PDFBibTeX XMLCite \textit{V. S. Vladimirov}, Russ. Math. Surv. 48, No. 6, 1 (1993; Zbl 0866.11068); translation from Usp. Mat. Nauk 48, No. 6(294), 3--38 (1993) Full Text: DOI
Andrijchuk, V. I. Pseudofinite fields and reciprocity law. (Ukrainian) Zbl 0956.11517 Mat. Stud. 2, 14-20 (1993). MSC: 11R58 11R56 PDFBibTeX XMLCite \textit{V. I. Andrijchuk}, Mat. Stud. 2, 14--20 (1993; Zbl 0956.11517)
Drakokhrust, Yu. A. On the group of conorms. (Russian. English summary) Zbl 0705.11074 Dokl. Akad. Nauk BSSR 34, No. 4, 293-296 (1990). Reviewer: I.Rosenknop MSC: 11S20 11R56 16K20 12J20 PDFBibTeX XMLCite \textit{Yu. A. Drakokhrust}, Dokl. Akad. Nauk BSSR 34, No. 4, 293--296 (1990; Zbl 0705.11074)
Katayama, Shin-ichi On unit groups of algebraic number fields. (English) Zbl 0669.12004 Proc. Japan Acad., Ser. A 64, No. 9, 345-346 (1988). Reviewer: W.Narkiewicz MSC: 11R27 PDFBibTeX XMLCite \textit{S.-i. Katayama}, Proc. Japan Acad., Ser. A 64, No. 9, 345--346 (1988; Zbl 0669.12004) Full Text: DOI
Igusa, Jun-ichi Zeta distributions associated with some invariants. (English) Zbl 0616.12006 Am. J. Math. 109, 1-33 (1987). Reviewer: S. Raghavan MSC: 11R56 11E45 11F27 11M41 11R47 PDFBibTeX XMLCite \textit{J.-i. Igusa}, Am. J. Math. 109, 1--33 (1987; Zbl 0616.12006) Full Text: DOI
Matthews, C. R. Spectral analysis of the action of ideles on adeles. (English) Zbl 0614.12009 J. Lond. Math. Soc., II. Ser. 32, 392-398 (1985). Reviewer: S.Gelbart MSC: 11R56 22E55 PDFBibTeX XMLCite \textit{C. R. Matthews}, J. Lond. Math. Soc., II. Ser. 32, 392--398 (1985; Zbl 0614.12009) Full Text: DOI
Chinburg, Ted Exact sequences and Galois module structure. (English) Zbl 0567.12010 Ann. Math. (2) 121, 351-376 (1985). Reviewer: R.W.van der Waall MSC: 11R33 11R32 16S34 PDFBibTeX XMLCite \textit{T. Chinburg}, Ann. Math. (2) 121, 351--376 (1985; Zbl 0567.12010) Full Text: DOI