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Tr. Mat. Inst. Steklova, 1999, Volume 224, Pages 122–129 (Mi tm694)  

This article is cited in 8 scientific papers (total in 9 papers)

Ramified Characters of Idèle Groups of One-Class Quadratic Fields

V. S. Vladimirov


Abstract: The necessary and sufficient conditions for the triviality of the ramified characters of the idèle group $A_d^\times $ of a one-class quadratic field $\mathbb Q(\sqrt d)$ on its multiplicative group $\mathbb Q^\times(\sqrt d)$ are established; i.e., the characters of the group $A_d^\times/\mathbb Q^\times(\sqrt d)$ are completely described.

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English version:
Proceedings of the Steklov Institute of Mathematics, 1999, 224, 107–114

Bibliographic databases:

Document Type: Article
UDC: 511.622:512.625.5:512.626.6
Received in September 1998

Citation: V. S. Vladimirov, “Ramified Characters of Idèle Groups of One-Class Quadratic Fields”, Algebra. Topology. Differential equations and their applications, Collection of papers dedicated to the 90th anniversary of academician Lev Semenovich Pontryagin, Tr. Mat. Inst. Steklova, 224, Nauka, MAIK Nauka/Inteperiodika, M., 1999, 122–129; Proc. Steklov Inst. Math., 224 (1999), 107–114

Citation in format AMSBIB
\Bibitem{Vla99}
\by V.~S.~Vladimirov
\paper Ramified Characters of Id\`ele Groups of One-Class Quadratic Fields
\inbook Algebra. Topology. Differential equations and their applications
\bookinfo Collection of papers dedicated to the 90th anniversary of academician Lev Semenovich Pontryagin
\serial Tr. Mat. Inst. Steklova
\yr 1999
\vol 224
\pages 122--129
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm694}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1721357}
\zmath{https://zbmath.org/?q=an:0956.11027}
\transl
\jour Proc. Steklov Inst. Math.
\yr 1999
\vol 224
\pages 107--114


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. S. Vladimirov, “Adelic Formulas for Gamma and Beta Functions of One-Class Quadratic Fields: Applications to 4-Particle Scattering String Amplitudes”, Proc. Steklov Inst. Math., 228 (2000), 67–80  mathnet  mathscinet  zmath
    2. S. V. Kozyrev, “Wavelet theory as $p$-adic spectral analysis”, Izv. Math., 66:2 (2002), 367–376  mathnet  crossref  crossref  mathscinet  zmath  elib
    3. A. A. Bolibrukh, A. A. Gonchar, I. V. Volovich, V. G. Kadyshevskii, A. A. Logunov, G. I. Marchuk, E. F. Mishchenko, S. M. Nikol'skii, S. P. Novikov, Yu. S. Osipov, L. D. Faddeev, D. V. Shirkov, “Vasilii Sergeevich Vladimirov (on his 80th birthday)”, Russian Math. Surveys, 58:1 (2003), 199–209  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. V. S. Vladimirov, “Adelic Formulas for Four-Particle String and Superstring Tree Amplitudes in One-Class Quadratic Fields”, Proc. Steklov Inst. Math., 245 (2004), 3–21  mathnet  mathscinet  zmath
    5. S. V. Kozyrev, “$p$-Adic Pseudodifferential Operators: Methods and Applications”, Proc. Steklov Inst. Math., 245 (2004), 143–153  mathnet  mathscinet  zmath
    6. S. V. Kozyrev, “Methods and Applications of Ultrametric and $p$-Adic Analysis: From Wavelet Theory to Biophysics”, Proc. Steklov Inst. Math., 274, suppl. 1 (2011), S1–S84  mathnet  crossref  crossref  zmath  isi  elib
    7. V. S. Vladimirov, “Regularized adelic formulas for string and superstring amplitudes in one-class quadratic fields”, Theoret. and Math. Phys., 164:3 (2010), 1101–1109  mathnet  crossref  crossref  adsnasa  isi
    8. A. Yu. Khrennikov, B. Nilsson, S. Nordebo, “Quantum rule for detection probability from Brownian motion in the space of classical fields”, Theoret. and Math. Phys., 174:2 (2013), 298–306  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. A. Kh. Bikulov, A. P. Zubarev, “Polnye sistemy sobstvennykh funktsii operatora Vladimirova v $L^{2}(B_r)$ i $L^{2}(\mathbb{Q}_{p})$”, Fundament. i prikl. matem., 21:3 (2016), 39–56  mathnet
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