Osipov, Denis V.; Parshin, Alekseĭ N. Harmonic analysis on the rank-2 value group of a two-dimensional local field. (English. Russian original) Zbl 1452.43005 Sb. Math. 211, No. 1, 115-160 (2020); translation from Mat. Sb. 211, No. 1, 125-174 (2020). MSC: 43A70 11S80 PDFBibTeX XMLCite \textit{D. V. Osipov} and \textit{A. N. Parshin}, Sb. Math. 211, No. 1, 115--160 (2020; Zbl 1452.43005); translation from Mat. Sb. 211, No. 1, 125--174 (2020) Full Text: DOI arXiv
Gorchinskiy, S. O.; Kulikov, Vik. S.; Parshin, A. N.; Popov, V. L. Igor Rostislavovich Shafarevich and his mathematical heritage. (English. Russian original) Zbl 1440.01025 Proc. Steklov Inst. Math. 307, 1-21 (2019); translation from Tr. Mat. Inst. Steklova 307, 9-31 (2019). MSC: 01A70 11-03 14-03 20-03 PDFBibTeX XMLCite \textit{S. O. Gorchinskiy} et al., Proc. Steklov Inst. Math. 307, 1--21 (2019; Zbl 1440.01025); translation from Tr. Mat. Inst. Steklova 307, 9--31 (2019) Full Text: DOI
Osipov, D. V.; Parshin, A. N. Representations of the discrete Heisenberg group on distribution spaces of two-dimensional local fields. (English. Russian original) Zbl 1377.11121 Proc. Steklov Inst. Math. 292, 185-201 (2016); translation from Tr. Mat. Inst. Steklova 292, 191-208 (2016). MSC: 11S23 11S85 20H05 20C15 PDFBibTeX XMLCite \textit{D. V. Osipov} and \textit{A. N. Parshin}, Proc. Steklov Inst. Math. 292, 185--201 (2016; Zbl 1377.11121); translation from Tr. Mat. Inst. Steklova 292, 191--208 (2016) Full Text: DOI arXiv
Parshin, A. N. On the direct image conjecture in the relative Langlands programme. (English. Russian original) Zbl 1371.14019 Russ. Math. Surv. 70, No. 5, 961-963 (2015); translation from Usp. Mat. Nauk 70, No. 5, 181-182 (2015). Reviewer: Paul Vojta (Berkeley) MSC: 14D24 22E57 11R39 PDFBibTeX XMLCite \textit{A. N. Parshin}, Russ. Math. Surv. 70, No. 5, 961--963 (2015; Zbl 1371.14019); translation from Usp. Mat. Nauk 70, No. 5, 181--182 (2015) Full Text: DOI
Parshin, A. N. A holomorphic version of the Tate-Iwasawa method for unramified \(L\)-functions. I. (English. Russian original) Zbl 1318.11149 Sb. Math. 205, No. 10, 1473-1491 (2014); translation from Mat. Sb. 205, No. 10, 107-124 (2014). Reviewer: Stelian Mihalas (Timişoara) MSC: 11R56 11R54 11M41 PDFBibTeX XMLCite \textit{A. N. Parshin}, Sb. Math. 205, No. 10, 1473--1491 (2014; Zbl 1318.11149); translation from Mat. Sb. 205, No. 10, 107--124 (2014) Full Text: DOI
Parshin, A. N. [Rezvyakova, Irina S.] Notes on the Poisson formula. With an appendix by Irina S. Rezvyakova. (English. Russian original) Zbl 1323.11065 St. Petersbg. Math. J. 23, No. 5, 781-818 (2012); translation from Algebra Anal. 23, No. 5, 1-54 (2011). MSC: 11M36 11M41 11R42 14G10 PDFBibTeX XMLCite \textit{A. N. Parshin}, St. Petersbg. Math. J. 23, No. 5, 781--818 (2012; Zbl 1323.11065); translation from Algebra Anal. 23, No. 5, 1--54 (2011) Full Text: DOI
Parshin, A. N. Questions and remarks to the Langlands programme. (English. Russian original) Zbl 1318.22010 Russ. Math. Surv. 67, No. 3, 509-539 (2012); translation from Usp. Mat. Nauk 67, No. 3, 115-146 (2012). Reviewer: Zongbin Chen (Lausanne) MSC: 22E57 11R39 11S37 11R70 14D24 PDFBibTeX XMLCite \textit{A. N. Parshin}, Russ. Math. Surv. 67, No. 3, 509--539 (2012; Zbl 1318.22010); translation from Usp. Mat. Nauk 67, No. 3, 115--146 (2012) Full Text: DOI arXiv
Osipov, D. V.; Parshin, A. N. Harmonic analysis and the Riemann-Roch theorem. (English. Russian original) Zbl 1350.14015 Dokl. Math. 84, No. 3, 826-829 (2011); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 441, No. 4, 444-448 (2011). Reviewer: Dmitri A. Timashev (Moskva) (MR2951489) MSC: 14C40 11R56 14G15 43A60 PDFBibTeX XMLCite \textit{D. V. Osipov} and \textit{A. N. Parshin}, Dokl. Math. 84, No. 3, 826--829 (2011; Zbl 1350.14015); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 441, No. 4, 444--448 (2011) Full Text: DOI arXiv
Parshin, A. N. Representations of higher adelic groups and arithmetic. (English) Zbl 1266.11118 Bhatia, Rajendra (ed.) et al., Proceedings of the international congress of mathematicians (ICM 2010), Hyderabad, India, August 19–27, 2010. Vol. I: Plenary lectures and ceremonies. Hackensack, NJ: World Scientific; New Delhi: Hindustan Book Agency (ISBN 978-981-4324-30-4/set; 978-81-85931-08-3/hbk; 978-981-4324-31-1/hbk; 978-981-4324-35-9/ebook). 362-392 (2011). Reviewer: V. Popa (Chişinău) MSC: 11R56 11S31 PDFBibTeX XMLCite \textit{A. N. Parshin}, in: Proceedings of the international congress of mathematicians (ICM 2010), Hyderabad, India, August 19--27, 2010. Vol. I: Plenary lectures and ceremonies. Hackensack, NJ: World Scientific; New Delhi: Hindustan Book Agency. 362--392 (2011; Zbl 1266.11118) Full Text: arXiv Link
Osipov, D. V.; Parshin, A. N. Harmonic analysis on local fields and adelic spaces. II. (English. Russian original) Zbl 1232.11122 Izv. Math. 75, No. 4, 749-814 (2011); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 75, No. 4, 91-164 (2011). Reviewer: V. Popa (Chisinau) MSC: 11R56 18B30 PDFBibTeX XMLCite \textit{D. V. Osipov} and \textit{A. N. Parshin}, Izv. Math. 75, No. 4, 749--814 (2011; Zbl 1232.11122); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 75, No. 4, 91--164 (2011) Full Text: DOI arXiv
Parshin, A. N. Notes on the Poisson formula. arXiv:1011.3392 Preprint, arXiv:1011.3392 [math.NT] (2010). MSC: 11Gxx 11Sxx 14Gxx 14Kxx BibTeX Cite \textit{A. N. Parshin}, ``Notes on the Poisson formula'', Preprint, arXiv:1011.3392 [math.NT] (2010) Full Text: arXiv OA License
Osipov, D. V.; Parshin, A. N. Harmonic analysis on local fields and adelic spaces. I. (English. Russian original) Zbl 1222.11137 Izv. Math. 72, No. 5, 915-976 (2008); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 72, No. 5, 77-140 (2008). Reviewer: V. Popa (Chisinau) MSC: 11R56 11S31 43A32 43A95 PDFBibTeX XMLCite \textit{D. V. Osipov} and \textit{A. N. Parshin}, Izv. Math. 72, No. 5, 915--976 (2008; Zbl 1222.11137); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 72, No. 5, 77--140 (2008) Full Text: DOI arXiv
Parshin, A. N. Higher dimensional local fields and \(L\)-functions. (English) Zbl 1008.11060 Fesenko, Ivan (ed.) et al., Invitation to higher local fields. Extended version of talks given at the conference on higher local fields, Münster, Germany, August 29-September 5, 1999. Coventry: Geometry and Topology Publications, Geom. Topol. Monogr. 3, 199-213 (2000). MSC: 11S40 11R56 11S80 PDFBibTeX XMLCite \textit{A. N. Parshin}, Geom. Topol. Monogr. 3, 199--213 (2000; Zbl 1008.11060) Full Text: EMIS
Parshin, A. N. Invitation to higher local fields, Part II, section 1: Higher dimensional local fields and L-functions. arXiv:math/0012151 Preprint, arXiv:math/0012151 [math.NT] (2000). MSC: 14G99 14G45 11M99 BibTeX Cite \textit{A. N. Parshin}, ``Invitation to higher local fields, Part II, section 1: Higher dimensional local fields and L-functions'', Preprint, arXiv:math/0012151 [math.NT] (2000) Full Text: arXiv
Fel’dman, N. I.; Nesterenko, Yu. V. Parshin, A. N. (ed.); Shafarevich, I. R. (ed.); Gamkrelidze, R. V. (ed.) Number theory IV: Transcendental numbers. Edited by A. N. Parshin, I. R. Shafarevich and R. V. Gamkrelidze. Transl. from the Russian by Neal Koblitz. (English) Zbl 0885.11004 Encyclopaedia of Mathematical Sciences 44. Berlin: Springer (ISBN 3-540-61467-2/hbk). 345 p. (1998). Reviewer: M.Waldschmidt (Paris) MSC: 11-02 11J81 11J82 11J86 11J25 11J85 11J89 11J68 PDFBibTeX XMLCite \textit{N. I. Fel'dman} et al., Number theory IV: Transcendental numbers. Edited by A. N. Parshin, I. R. Shafarevich and R. V. Gamkrelidze. Transl. from the Russian by Neal Koblitz. Berlin: Springer (1998; Zbl 0885.11004)
Parshin, A. N. (ed.); Shafarevich, I. R. (ed.); Gamkrelidze, R. V. (ed.) Number theory IV: Transcendental numbers. Transl. from the Russian by N. Koblitz. (English) Zbl 1155.00324 Encyclopaedia of Mathematical Sciences 44. Berlin: Springer (ISBN 3-540-61467-2/hbk). 345 p. (1998). MSC: 00B15 11-02 11J81 PDFBibTeX XMLCite \textit{A. N. Parshin} (ed.) et al., Number theory IV: Transcendental numbers. Transl. from the Russian by N. Koblitz. Berlin: Springer (1998; Zbl 1155.00324)
Arslanov, M. M. (ed.); Parshin, A. N. (ed.); Shafarevich, I. R. (ed.) Algebra and analysis. Proceedings of the international centennial Chebotarev conference, Kazan, Russia, June 5-11, 1994. (English) Zbl 0859.00022 Berlin: Walter de Gruyter. viii, 163 p. (1996). MSC: 00B25 17-06 14-06 11-06 PDFBibTeX XMLCite \textit{M. M. Arslanov} (ed.) et al., Algebra and analysis. Proceedings of the international centennial Chebotarev conference, Kazan, Russia, June 5-11, 1994. Berlin: Walter de Gruyter (1996; Zbl 0859.00022)
Parshin, A. N. (ed.); Shafarevich, I. R. (ed.); Gamkrelidze, R. V. (ed.) Number theory I: fundamental problems, ideas and theories. Transl. from the Russian by A. A. Panchishkin. (English) Zbl 0827.00016 Encyclopaedia of Mathematical Sciences. 49. Berlin: Springer-Verlag. 303 p. (1995). MSC: 00B15 11-06 PDFBibTeX XMLCite \textit{A. N. Parshin} (ed.) et al., Number theory I: fundamental problems, ideas and theories. Transl. from the Russian by A. A. Panchishkin. Berlin: Springer-Verlag (1995; Zbl 0827.00016)
Parshin, A. N. (ed.); Shafarevich, I. R. (ed.); Gamkrelidze, R. V. (ed.) Number theory II: Algebraic number theory. Transl. from the Russian. (English) Zbl 0814.00007 Encyclopaedia of Mathematical Sciences. 62. Berlin: Springer-Verlag. 269 p. (1992). MSC: 00B15 11-06 PDFBibTeX XMLCite \textit{A. N. Parshin} (ed.) et al., Number theory II: Algebraic number theory. Transl. from the Russian. Berlin: Springer-Verlag (1992; Zbl 0814.00007)
Parshin, A. N. Galois cohomology and the Brauer group of local fields. (English. Russian original) Zbl 0731.11064 Proc. Steklov Inst. Math. 183, 191-201 (1991); translation from Tr. Mat. Inst. Steklova 183, 159-169 (1990). Reviewer: K.Szymiczek (Tychy) MSC: 11S31 12G05 12G10 11S70 14F22 11S25 11S15 PDFBibTeX XMLCite \textit{A. N. Parshin}, Proc. Steklov Inst. Math. 183, 191--201 (1991; Zbl 0731.11064); translation from Tr. Mat. Inst. Steklova 183, 159--169 (1990)
Gamkrelidze, R. V. (ed.); Parshin, A. N. (ed.); Shafarevich, I. R. (ed.) Number theory - 1. (Teoriya chisel - 1.) (Russian) Zbl 0694.00004 Itogi Nauki i Tekhniki. Seriya: Sovremennye Problemy Matematiki. Fundamental’nye Napravleniya, 49. Moskva: Vsesoyuznyj Institut Nauchnoj i Tekhnicheskoj Informatsii. 348 p. R. 2.60 (1990). MSC: 00Bxx 11-06 PDFBibTeX XMLCite \textit{R. V. Gamkrelidze} (ed.) et al., Teoriya chisel - 1 (Russian). Moskva: Vsesoyuznyj Institut Nauchnoj i Tekhnicheskoj Informatsii (1990; Zbl 0694.00004)
Parshin, A. N. On the application of ramified coverings in the theory of diophantine equations. (English. Russian original) Zbl 0702.14017 Math. USSR, Sb. 66, No. 1, 249-264 (1990); translation from Mat. Sb. 180, No. 2, 244-259 (1989). Reviewer: S.Kotov MSC: 14G40 14E20 14H25 14G05 11D41 PDFBibTeX XMLCite \textit{A. N. Parshin}, Math. USSR, Sb. 66, No. 1, 249--264 (1990; Zbl 0702.14017); translation from Mat. Sb. 180, No. 2, 244--259 (1989) Full Text: DOI
Parshin, A. N. The Bogomolov-Miyaoka-Yau inequality for the arithmetical surfaces and its applications. (English) Zbl 0706.14015 Sémin. Théor. Nombres, Paris 1986-87, Prog. Math. 75, 299-312 (1988). Reviewer: R.-P.Holzapfel MSC: 14G40 14H52 14J20 11D25 PDFBibTeX XML
Ireland, Kenneth F.; Rosen, Michael I. Parshin, A. N. (ed.) A classical introduction to modern number theory. Transl. from the English by S. P. Demushkin. Translation edited and with a preface by A. N. Parshin. (Классическое введение в современную теорию чисел.) (Russian) Zbl 0662.10001 Moskva: Mir. 416 p. R. 2.00 (1987). MSC: 11-01 12-01 PDFBibTeX XML
Zarkhin, Yu. G.; Parshin, A. N. Finiteness problems in Diophantine geometry. (English. Russian original) Zbl 0672.14012 Transl., II. Ser., Am. Math. Soc. 143, 35-102 (1989); translation from Appendix to the Russian translation of the book of Serge Lang: “Fundamentals of Diophantine geometry”, Mir, Moscow, 396-438 (1986). MSC: 14Gxx 14-02 11D41 14H52 14K15 14G05 PDFBibTeX XML Full Text: arXiv
Lang, Serge Manin, Yu. I. (ed.) [Zarkhin, Yu. G.; Parshin, A. N.; Markushevich, D. G.] Fundamentals of Diophantine geometry. (Osnovy diofantovoj geometrii). Transl. from the English by D. G. Markushevich. Transl. ed. and with a preface by Yu. I. Manin. With an appendix by Yu. G. Zarkhin and A. N. Parshin. (Russian) Zbl 0644.14007 Moskva: Mir. 448 p. R. 2.90 (1986). MSC: 14Gxx 14-02 14K15 11D41 14G05 PDFBibTeX XML
Parshin, A. N.; Shafarevich, I. R. The arithmetic of algebraic varieties (in the algebra section of the Steklov mathematical institute of the academy of sciences). (English. Russian original) Zbl 0605.14001 Proc. Steklov Inst. Math. 168, 75-99 (1986); translation from Tr. Mat. Inst. Steklova 168, 72-97 (1984). Reviewer: J.Dieudonné MSC: 14-03 14Gxx 14Kxx 01A60 11Fxx PDFBibTeX XMLCite \textit{A. N. Parshin} and \textit{I. R. Shafarevich}, Proc. Steklov Inst. Math. 168, 75--99 (1986; Zbl 0605.14001); translation from Tr. Mat. Inst. Steklova 168, 72--97 (1984)
Parshin, A. N. Local class field theory. (English) Zbl 0579.12012 Proc. Steklov Inst. Math. 165, 157-185 (1985). MSC: 11S31 11S70 18F25 11T99 14F22 14G20 PDFBibTeX XMLCite \textit{A. N. Parshin}, Proc. Steklov Inst. Math. 165, 157--185 (1985; Zbl 0579.12012)
Parshin, A. N. Local class field theory. (Russian) Zbl 0535.12013 Tr. Mat. Inst. Steklova 165, 143-170 (1984). MSC: 11S31 11S70 14G20 18F25 11T99 14F22 PDFBibTeX XMLCite \textit{A. N. Parshin}, Tr. Mat. Inst. Steklova 165, 143--170 (1984; Zbl 0535.12013)
Parshin, A. N. Chern classes, adeles and L-functions. (English) Zbl 0518.14013 J. Reine Angew. Math. 341, 174-192 (1983). MSC: 14G10 14J20 57R20 11R56 PDFBibTeX XMLCite \textit{A. N. Parshin}, J. Reine Angew. Math. 341, 174--192 (1983; Zbl 0518.14013) Full Text: DOI Crelle EuDML
Bashmakova, I. G.; Gnedenko, B. V.; Kuzicheva, Z. A.; Medvedev, F. A.; Ozhigova, E. P.; Parshin, A. N.; Rudakov, A. N.; Slavutin, E. I.; Sheĭnin, O. B.; Yushkevich, A. P. Kolmogorov, A. N. (ed.); Yushkevich, A. P. (ed.) XIXth century mathematics. Mathematical logic. Algebra. Number theory. Probability theory. Ed. by A. N. Kolmogorov and A. P. Yushkevich. (Математика {XIX} века. Математическая логика. Алгебра. Теория чисел. Теория вероятностей.) (Russian) Zbl 0523.01001 Moskva: “Nauka”. 255 p. R. 2.10 (1978). Reviewer: Ivor Grattan-Guinness (Bengeo) (M.R. 80i:01010) MSC: 01A05 01-02 01A55 03-03 11-03 15-03 60-03 PDFBibTeX XML
Parshin, A. N. Abelian coverings of arithmetic schemes. (English. Russian original) Zbl 0443.12006 Sov. Math., Dokl. 19, 1438-1442 (1978); translation from Dokl. Akad. Nauk SSSR 243, 855-858 (1978). MSC: 11S31 11S15 14A15 12G05 PDFBibTeX XMLCite \textit{A. N. Parshin}, Sov. Math., Dokl. 19, 1438--1442 (1978; Zbl 0443.12006); translation from Dokl. Akad. Nauk SSSR 243, 855--858 (1978)
Parshin, A. N. Klassenkörper und algebraische K-Theorie. (Russian) Zbl 0302.14005 Usp. Mat. Nauk 30, No. 1(181), 253-254 (1975). MSC: 14C35 14E20 11R37 11S31 18F25 PDFBibTeX XMLCite \textit{A. N. Parshin}, Usp. Mat. Nauk 30, No. 1(181), 253--254 (1975; Zbl 0302.14005)