Chirskii, V. G. Transcendence of \(p\)-adic values of generalized hypergeometric series with transcendental polyadic parameters. (English. Russian original) Zbl 07735230 Dokl. Math. 107, No. 2, 109-111 (2023); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 510, 29-32 (2023). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J91 11J61 11J81 11J85 PDFBibTeX XMLCite \textit{V. G. Chirskii}, Dokl. Math. 107, No. 2, 109--111 (2023; Zbl 07735230); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 510, 29--32 (2023) Full Text: DOI
Bugeaud, Yann; Kekeç, Gülcan On Sprindžuk’s classification of \(p\)-adic numbers. (English) Zbl 1477.11125 J. Aust. Math. Soc. 111, No. 2, 221-231 (2021). Reviewer: István Gaál (Debrecen) MSC: 11J61 11J82 PDFBibTeX XMLCite \textit{Y. Bugeaud} and \textit{G. Kekeç}, J. Aust. Math. Soc. 111, No. 2, 221--231 (2021; Zbl 1477.11125) Full Text: DOI
Coray, Daniel Notes on geometry and arithmetic. Translated from the French by John Steinig and Constantin Manoil. (English) Zbl 1457.11001 Universitext. Cham: Springer (ISBN 978-3-030-43780-0/pbk; 978-3-030-43781-7/ebook). xii, 181 p. (2020). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11-01 14-01 11Jxx 11Gxx 14Gxx PDFBibTeX XMLCite \textit{D. Coray}, Notes on geometry and arithmetic. Translated from the French by John Steinig and Constantin Manoil. Cham: Springer (2020; Zbl 1457.11001) Full Text: DOI
Dalloul, Amran On \(p\)-adic continued frations. (English) Zbl 1416.11125 JP J. Algebra Number Theory Appl. 40, No. 5, 875-886 (2018). MSC: 11J70 11Y65 11S99 PDFBibTeX XMLCite \textit{A. Dalloul}, JP J. Algebra Number Theory Appl. 40, No. 5, 875--886 (2018; Zbl 1416.11125) Full Text: DOI
Almira, J. M. An ultrametric lethargy result and its application to \(p\)-adic number theory. (English) Zbl 1290.46066 Bull. Malays. Math. Sci. Soc. (2) 36, No. 4, 927-935 (2013). Reviewer: T. D. Narang (Amritsar) MSC: 46S10 41A65 11J61 11J81 11K60 PDFBibTeX XMLCite \textit{J. M. Almira}, Bull. Malays. Math. Sci. Soc. (2) 36, No. 4, 927--935 (2013; Zbl 1290.46066) Full Text: arXiv Link
Krattenthaler, C.; Rivoal, T. Multivariate \(p\)-adic formal congruences and integrality of Taylor coefficients of mirror maps. (English. French summary) Zbl 1308.11099 Di Vizio, Lucia (ed.) et al., Arithmetic and Galois theories of differential equations. Proceedings of the summer school, ‘Galoisian and arithmetic theory of differential equations’, CIRM, Luminy, France, September 21–25, 2009. Paris: Société Mathématique de France (ISBN 978-2-85629-331-7/pbk). Séminaires et Congrès 23, 241-269 (2011). MSC: 11S80 11J99 14J32 33C70 PDFBibTeX XMLCite \textit{C. Krattenthaler} and \textit{T. Rivoal}, Sémin. Congr. 23, 241--269 (2011; Zbl 1308.11099) Full Text: arXiv
Nesterenko, Yu. V. Algebraic independence of \(p\)-adic numbers. (English. Russian original) Zbl 1145.11055 Izv. Math. 72, No. 3, 565-579 (2008); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 72, No. 3, 159-174 (2008). Reviewer: Maurice Mignotte (Strasbourg) MSC: 11J85 11J81 PDFBibTeX XMLCite \textit{Yu. V. Nesterenko}, Izv. Math. 72, No. 3, 565--579 (2008; Zbl 1145.11055); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 72, No. 3, 159--174 (2008) Full Text: DOI
Vâjâitu, Marian; Zaharescu, Alexandru Trace functions and Galois invariant \(p\)-adic measures. (English) Zbl 1131.11076 Publ. Mat., Barc. 50, No. 1, 43-55 (2006). Reviewer: Gabriel D. Villa-Salvador (México D.F.) MSC: 11S80 12F20 PDFBibTeX XMLCite \textit{M. Vâjâitu} and \textit{A. Zaharescu}, Publ. Mat., Barc. 50, No. 1, 43--55 (2006; Zbl 1131.11076) Full Text: DOI EuDML
Steuding, Jörn Diophantine analysis. (English) Zbl 1101.11022 Discrete Mathematics and its Applications. Boca Raton, FL: Chapman & Hall/CRC (ISBN 1-58488-482-7/hbk). 261 p. (2005). Reviewer: Christian Elsholtz (Surrey) MSC: 11Jxx 11-02 11-01 11Dxx 11Hxx 11Sxx PDFBibTeX XMLCite \textit{J. Steuding}, Diophantine analysis. Boca Raton, FL: Chapman \& Hall/CRC (2005; Zbl 1101.11022)
Ito, Tetsushi Birational smooth minimal models have equal Hodge numbers in all dimensions. (English) Zbl 1051.14012 Yui, Noriko (ed.) et al., Calabi-Yau varieties and mirror symmetry. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3355-3/hbk). Fields Inst. Commun. 38, 183-194 (2003). Reviewer: Massimiliano Mella (Ferrara) MSC: 14E05 14C30 11S80 14E30 PDFBibTeX XMLCite \textit{T. Ito}, Fields Inst. Commun. 38, 183--194 (2003; Zbl 1051.14012) Full Text: arXiv
Alexandru, Victor; Zaharescu, Alexandru A transcendence criterion over \(p\)-adic fields. (English) Zbl 1042.11047 Nihonkai Math. J. 14, No. 2, 83-93 (2003). Reviewer: Gabriel D. Villa-Salvador (México D.F.) MSC: 11J61 11S99 12F20 12J25 PDFBibTeX XMLCite \textit{V. Alexandru} and \textit{A. Zaharescu}, Nihonkai Math. J. 14, No. 2, 83--93 (2003; Zbl 1042.11047)
Wang, Chin-Lung Cohomology theory in birational geometry. (English) Zbl 1052.14016 J. Differ. Geom. 60, No. 2, 345-354 (2002). Reviewer: Vladimir L. Popov (Moskva) MSC: 14C30 14E05 PDFBibTeX XMLCite \textit{C.-L. Wang}, J. Differ. Geom. 60, No. 2, 345--354 (2002; Zbl 1052.14016) Full Text: DOI
Matala-aho, Tapani On Diophantine approximations of the solutions of \(q\)-functional equations. (English) Zbl 1007.39019 Proc. R. Soc. Edinb., Sect. A, Math. 132, No. 3, 639-659 (2002). Reviewer: Claudi Alsina (Barcelona) MSC: 39B22 11J99 PDFBibTeX XMLCite \textit{T. Matala-aho}, Proc. R. Soc. Edinb., Sect. A, Math. 132, No. 3, 639--659 (2002; Zbl 1007.39019) Full Text: DOI
Alexandru, Victor; Popescu, Nicolae; Zaharescu, Alexandru Trace on \(\mathbb{C}_p\). (English) Zbl 0965.11049 J. Number Theory 88, No. 1, 13-38 (2001). Reviewer: Gabriel D.Villa-Salvador (México) MSC: 11S80 12F20 PDFBibTeX XMLCite \textit{V. Alexandru} et al., J. Number Theory 88, No. 1, 13--38 (2001; Zbl 0965.11049) Full Text: DOI
Burger, Edward B. Exploring the number jungle: A journey into diophantine analysis. (English) Zbl 0973.11001 Student Mathematical Library. 8. Providence, RI: American Mathematical Society (AMS). vi, 151 p. (2000). Reviewer: Peter Bundschuh (Köln) MSC: 11-01 11Jxx 11Hxx 11Dxx 11H06 11G05 11J70 11J82 11D45 11J06 11F85 PDFBibTeX XMLCite \textit{E. B. Burger}, Exploring the number jungle: A journey into diophantine analysis. Providence, RI: American Mathematical Society (AMS) (2000; Zbl 0973.11001)
Goldman, Jay R. The queen of mathematics: a historically motivated guide to number theory. (English) Zbl 0890.11001 Wellesley, MA: A K Peters. xxiv, 525 p. (1998). Reviewer: H.Opolka (Braunschweig) MSC: 11-01 11-03 11Axx 11Dxx 01-01 11Hxx 11Jxx 11Rxx 11Gxx 11Exx PDFBibTeX XMLCite \textit{J. R. Goldman}, The queen of mathematics: a historically motivated guide to number theory. Wellesley, MA: A K Peters (1998; Zbl 0890.11001)
Totaro, Burt Tensor products in \(p\)-adic Hodge theory. (English) Zbl 0873.14019 Duke Math. J. 83, No. 1, 79-104 (1996). MSC: 14F30 14C30 14G20 PDFBibTeX XMLCite \textit{B. Totaro}, Duke Math. J. 83, No. 1, 79--104 (1996; Zbl 0873.14019) Full Text: DOI
Sprindzhuk, Vladimir G. Classical diophantine equations. (English) Zbl 0787.11008 Lecture Notes in Mathematics. 1559. Berlin: Springer-Verlag. xii, 228 p. (1993). Reviewer: R.P.Steiner (Bowling Green) MSC: 11Dxx 11Jxx 11-02 11R09 11R29 14Gxx PDFBibTeX XMLCite \textit{V. G. Sprindzhuk}, Classical diophantine equations. Berlin: Springer-Verlag (1993; Zbl 0787.11008)
Schlickewei, Hans Peter Multiplicities of algebraic linear recurrences. (English) Zbl 0789.11012 Acta Math. 170, No. 2, 151-180 (1993). Reviewer: I.Gaál (Debrecen) MSC: 11B37 11J99 11R04 PDFBibTeX XMLCite \textit{H. P. Schlickewei}, Acta Math. 170, No. 2, 151--180 (1993; Zbl 0789.11012) Full Text: DOI
Oryan, M. H. Über gewisse Potenzreihen, deren Funktionswerte für Argumente aus der Menge der p-adischen Liouvilleschen Zahlen p-adische U-Zahlen vom Grade \(\leq m\) sind. (On certain power series whose function values for arguments from the set of p-adic Liouville numbers are p-adic U-numbers of degree \(\leq m)\). (German) Zbl 0706.11037 Rev. Fac. Sci. Univ. Istanbul, Sér. A 47(1986), 53-67 (1990). Reviewer: P.Bundschuh MSC: 11J82 PDFBibTeX XMLCite \textit{M. H. Oryan}, Rev. Fac. Sci. Univ. Istanbul, Sér. A 47, 53--67 (1990; Zbl 0706.11037)
Yuan, Jing Approximation theorem on p-adic algebraic numbers. (Chinese. English summary) Zbl 0676.10022 J. Northwest Univ., Nat. Sci. 18, No. 4, 38-41 (1988). Reviewer: M.-C.Liu MSC: 11J68 11J81 PDFBibTeX XML
Zeren, B. M. On certain complex and \(p\)-adic power series with values in Mahler’s subclasses \(U_ m\). (Über einige komplexe und \(p\)-adische Lückenreihen mit Werten aus den Mahlerschen Unterklassen \(U_ m\).) (German) Zbl 0665.10024 Rev. Fac. Sci. Univ. Istanbul, Sér. A 45(1980), 89-130 (1988). Reviewer: Wolfgang Haneke (Marburg) MSC: 11J81 11J61 PDFBibTeX XMLCite \textit{B. M. Zeren}, Rev. Fac. Sci. Univ. Istanbul, Sér. A 45, 89--130 (1988; Zbl 0665.10024)
Oryan, M. H. On certain power series taking values from Mahler’s subclass \(U_ m\) for algebraic arguments. (Über gewisse Potenzreihen, die für algebraische Argumente Werte aus den Mahlerschen Unterklassen \(U_ m\) nehmen.) (German) Zbl 0665.10022 Rev. Fac. Sci. Univ. Istanbul, Sér. A 45(1980), 1-42 (1988). Reviewer: Wolfgang Haneke (Marburg) MSC: 11J81 11J61 PDFBibTeX XMLCite \textit{M. H. Oryan}, Rev. Fac. Sci. Univ. Istanbul, Sér. A 45, 1--42 (1988; Zbl 0665.10022)
Laohakosol, Vichian; Ubolsri, Patchara Continued fractions representing transcendental numbers. (English) Zbl 0608.10033 Bull. Malays. Math. Soc., II. Ser. 9, 1-21 (1986). Reviewer: F.Schweiger MSC: 11J81 11J70 11J61 PDFBibTeX XMLCite \textit{V. Laohakosol} and \textit{P. Ubolsri}, Bull. Malays. Math. Soc., II. Ser. 9, 1--21 (1986; Zbl 0608.10033)
Wang, Lianxiang \(p\)-adic continued fractions. I, II. (English) Zbl 0628.10036 Sci. Sin., Ser. A 28, 1009-1017 (1985); 28, 1018-1023 (1985). Reviewer: François Gramain (Saint-Etienne) MSC: 11J70 11J61 11J81 11J85 PDFBibTeX XMLCite \textit{L. Wang}, Sci. Sin., Ser. A 28, 1009--1017, 1018--1023 (1985; Zbl 0628.10036)
Crew, Richard On torsion in the slope spectral sequence. (English) Zbl 0618.14007 Compos. Math. 56, 79-86 (1985). MSC: 14F30 14C30 PDFBibTeX XMLCite \textit{R. Crew}, Compos. Math. 56, 79--86 (1985; Zbl 0618.14007) Full Text: Numdam EuDML
Parent, D. P. Exercises in number theory. Translation from the French. (English) Zbl 0536.10001 Problem Books in Mathematics. New York etc.: Springer-Verlag. x, 541 p. DM 135.00; $ 47.40 (1984). Reviewer: Olaf Ninnemann (Berlin) MSC: 11-01 00A07 PDFBibTeX XML
Narkiewicz, W. Number theory. Transl. from the Polish by S. Kanemitsu. (English) Zbl 0528.10001 Singapore: World Scientific. xii, 371 p. £17.00 (1983). Reviewer: Wolfgang Schwarz (Frankfurt am Main) MSC: 11-01 11Axx 11Hxx 11Jxx 11Mxx 11Pxx 11Kxx 11R04 11S85 PDFBibTeX XML
Escassut, Alain Numbers with order \(\leq 1\). (English) Zbl 0511.12016 Groupe Etude Anal. Ultrametrique 9e Annee: 1981/82, No. 3, Expose J6, 4 p. (1983). MSC: 12F20 12J10 11J81 11S05 PDFBibTeX XML Full Text: Numdam EuDML
Sprindzhuk, V. G. Classical diophantine equations in two unknowns. (Классические диофантовы уравнения от двух неизвестных.) (Russian) Zbl 0523.10008 Moskva: “Nauka” Glavnaya Redaktsiya Fiziko-Matematicheskoĭ Literatury. 288 p. R. 2.60 (1982). Reviewer: Ray Phillip Steiner (Bowling Green) MSC: 11Dxx 11-02 11Jxx 11D25 11D41 11D57 11D59 11D61 11D85 11D88 11J86 11R29 11J68 11J81 11J61 PDFBibTeX XML
Bertrand, Daniel Problèmes de transcendance lies aux hauteurs sur les courbes elliptiques. (French) Zbl 0495.10023 Mathematiques, Bull. Sect. Sci. III, 55-63 (1981). MSC: 11J81 14H52 14G05 11J85 14H45 PDFBibTeX XML
Sprindzhuk, V. G. Achievements and problems in diophantine approximation theory. (English) Zbl 0463.10020 Russ. Math. Surv. 35, No. 4, 1-80 (1980). MSC: 11Jxx 11-02 11K60 11Dxx 11R23 PDFBibTeX XMLCite \textit{V. G. Sprindzhuk}, Russ. Math. Surv. 35, No. 4, 1--80 (1980; Zbl 0463.10020) Full Text: DOI
Katz, Nicholas M. Slope filtration of F-crystals. (English) Zbl 0426.14007 Astérisque 63, 113-164 (1979). MSC: 14F30 14C30 13K05 PDFBibTeX XMLCite \textit{N. M. Katz}, Astérisque 63, 113--164 (1979; Zbl 0426.14007)
Narkiewicz, Wladyslaw Number theory. (Teoria liczb.) (Polish) Zbl 0422.10001 Biblioteka Matematyczna, Tom 50. Warszawa: Panstwowe Wydawnictwo Naukowe. 355 p. Zl. 75.00 (1977). Reviewer: Shigeru Kanemitsu (Kayanomori / Iizuka) MSC: 11-01 11Axx 11Hxx 11Jxx 11Mxx 11Nxx 11Pxx 11Kxx 11R04 11S05 PDFBibTeX XML
Rieger, Georg Johann Number theory. (Zahlentheorie.) (German) Zbl 0328.10001 Studia Mathematica/Mathematische Lehrbücher. Band XXIX. Göttingen: Vandenhoeck & Ruprecht. 219 S. DM 39.00 (1976). Reviewer: Herbert Pieper (Berlin) MSC: 11-01 11Axx 11Mxx 11Jxx 11Pxx 11N05 11N13 11M06 11N35 11P05 PDFBibTeX XML
Bertrand, Daniel Equations différentielles algébriques et nombres transcendants dans les domaines complexe et p-adique. (French) Zbl 0391.10026 Paris: Universite de Paris VI. V, 46 p. (1975). MSC: 11J81 12H20 11S80 11J85 11J61 12H25 PDFBibTeX XML
Sprindzhuk, V. G. The measure of the set of \(S\)-numbers in the \(p\)-adic field. (English. Russian original) Zbl 0146.27702 Sov. Math., Dokl. 4, 1201-1202 (1963); translation from Dokl. Akad. Nauk SSSR 151, 1292 (1963). Reviewer: V. G. Sprindzhuk (R. Zh. Mat. 1964, 1A162) MSC: 11J82 11J68 PDFBibTeX XMLCite \textit{V. G. Sprindzhuk}, Sov. Math., Dokl. 4, 1201--1202 (1963; Zbl 0146.27702); translation from Dokl. Akad. Nauk SSSR 151, 1292 (1963)
Gelfond, A. O. Transcendental and algebraic numbers. (English. Russian original) Zbl 0090.26103 New York: Dover Publications, Inc. vii, 190 p. (1960). MSC: 11J81 11J82 11-01 11J17 11J61 11J68 11J89 11J91 PDFBibTeX XML
Günther, Alfred Über transzendente \(\mathfrak p\)-adische Zahlen. II: Zur Approximation transzendenter \(\mathfrak p\)-adischer Zahlen durch rationale. (German) Zbl 0055.27703 J. Reine Angew. Math. 193, 1-10 (1954). MSC: 11J81 11J61 PDFBibTeX XMLCite \textit{A. Günther}, J. Reine Angew. Math. 193, 1--10 (1954; Zbl 0055.27703) Full Text: DOI Crelle EuDML
Günther, Alfred Über transzendentale \({\mathfrak p}\)-adische Zahlen. I: Ein Satz über algebraische Abhängigkeit \({\mathfrak p}\)-adischer Funktionen als Prinzip für Transzendenzbeweise \({\mathfrak p}\)-adischer Zahlen. (German) Zbl 0055.04504 J. Reine Angew. Math. 192, 155-166 (1954). Reviewer: Kurt Mahler MSC: 11J81 11J61 PDFBibTeX XMLCite \textit{A. Günther}, J. Reine Angew. Math. 192, 155--166 (1954; Zbl 0055.04504) Full Text: Crelle EuDML
Gel’fond, A. O. Transcendental and algebraic numbers. (Трансцендентные и алгебраические числа) (Transzendente und algebraische Zahlen.) (Russian) Zbl 0048.03303 Moskva: Gosudarstv. Izdat. Tekhn.-Teor. Lit., 224 p. (1952). Reviewer: Kurt Mahler (Manchester) MSC: 11J81 11J82 11-01 11J17 11J61 11J68 11J89 11J91 PDFBibTeX XML
Mahler, Kurt On transcendental \(p\)-adic numbers. (Über transzendente \(p\)-adische Zahlen.) (German) Zbl 0012.05302 Compos. Math. 2, 259-275 (1935). Reviewer: J. F. Koksma (Amsterdam) MSC: 11J81 11J61 PDFBibTeX XMLCite \textit{K. Mahler}, Compos. Math. 2, 259--275 (1935; Zbl 0012.05302) Full Text: Numdam EuDML
Gelfond, A. Sur le septième problème de D. Hilbert. (Russian, French) JFM 60.0163.04 C. R. Acad. Sc. URSS (2) 2, 1-6 (1934). Reviewer: Schneider, T., Dr. (Frankfurt am Main) MSC: 11J81 11J61 PDFBibTeX XMLCite \textit{A. Gelfond}, C. R. (Dokl.) Acad. Sci. URSS, n. Ser. 1934, No. 2, 1--6 (1934; JFM 60.0163.04)