Edit Profile (opens in new tab) Carmichael, Robert D. (b. 1879 d. 1967) Co-Author Distance Author ID: carmichael.robert-d Published as: Carmichael, R. D.; Carmichael, Robert D. External Links: MacTutor · MGP · Wikidata · GND · IdRef Documents Indexed: 176 Publications since 1906, including 17 Books Co-Authors: 10 Co-Authors with 9 Joint Publications 24 Co-Co-Authors all top 5 Co-Authors 167 single-authored 2 Martin, William Ted 2 Mason, Thomas Edward 2 Smith, Edwin Raymond 2 Weaver, James H. 1 Bird, M. R. 1 Bird, Marion T. 1 Davis, Harold T. 1 Hufford, Mason E. 1 La Paz, Lincoln 1 MacMillan, William Duncan all top 5 Serials 81 Bulletin of the American Mathematical Society 21 American Journal of Mathematics 19 American Mathematical Monthly 13 Annals of Mathematics. Second Series 7 Transactions of the American Mathematical Society 4 Tohoku Mathematical Journal 2 Duke Mathematical Journal 2 Physical Review, II. Series 2 Proceedings of the London Mathematical Society. Second Series 2 The Quarterly Journal of Mathematics. Oxford Series 2 The Quarterly Journal of Pure and Applied Mathematics 1 Proceedings of the National Academy of Sciences of the United States of America 1 Physical Review all top 5 Fields 18 Number theory (11-XX) 3 Group theory and generalizations (20-XX) 2 Combinatorics (05-XX) 2 Difference and functional equations (39-XX) 2 Relativity and gravitational theory (83-XX) 1 General and overarching topics; collections (00-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX) 1 Real functions (26-XX) 1 Geometry (51-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 57 Publications have been cited 555 times in 517 Documents Cited by ▼ Year ▼ The general theory of linear \(q\)-difference equations. JFM 43.0411.02Carmichael, R. D. 104 1912 On the numerical factors of the arithmetic forms \(\alpha^n\pm \beta^n\). JFM 44.0216.01Carmichael, R. D. 94 1913 Introduction to the theory of groups of finite order. Zbl 0019.19702Carmichael, R. D. 72 1937 Note on a new number theory function. JFM 41.0226.04Carmichael, R. D. 40 1910 Introduction to the theory of groups of finite order. 2nd edition. Zbl 0075.23901Carmichael, Robert D. 31 1956 Linear difference equations and their analytic solutions. JFM 42.0359.01Carmichael, R. D. 16 1911 On the numerical factors of the arithmetic forms \(\alpha^n\pm \beta^n\). JFM 45.1259.10Carmichael, R. D. 15 1914 Expansions of arithmetical functions in infinite series. Zbl 0004.29305Carmichael, R. D. 13 1932 Note on Euler’s \(\varphi\)-function. JFM 48.0158.04Carmichael, R. D. 13 1922 Note on the roots of algebraic equations. JFM 45.0168.01Carmichael, R. D.; Mason, T. E. 13 1914 Linear differential equations of infinite order. Zbl 0014.26004Carmichael, R. D. 10 1936 On composite numbers \(P\) which satisfy the Fermat congruence \(a^{P-1}\equiv 1\pmod P\). JFM 42.0236.07Carmichael, R. D. 10 1911 The theory of numbers. JFM 45.0283.10Carmichael, R. D. 9 1914 On Euler’s \(\varphi\)-function. JFM 38.0236.01Carmichael, R. D. 9 1907 Diophantine analysis. JFM 45.0283.11Carmichael, R. D. 8 1915 Abstract definitions of the symmetric and alternating groups and certain other permutation groups. JFM 48.1148.03Carmichael, R. D. 7 1922 The theory of numbers and Diophantine analysis. Unabridged and unaltered republ. of the latest ed. Zbl 0086.01104Carmichael, Robert D. 6 1959 Boundary value and expansion problems: algebraic basis of the theory. JFM 48.0522.01Carmichael, R. D. 6 1921 On the theory of linear difference equations. JFM 44.0397.03Carmichael, R. D. 6 1913 Expansions of arithmetical functions in infinite series. JFM 58.0184.01Carmichael, R. D. 5 1932 Tactical configurations of rank two. Zbl 0001.01002Carmichael, R. D. 4 1931 Systems of linear difference equations and expansions in series of exponential functions. Zbl 0006.16901Carmichael, R. D. 4 1933 Algebras of certain doubly transitive groups. Zbl 0002.01102Carmichael, R. D. 3 1931 Introduction to the theory of groups of finite order. JFM 63.0860.01Carmichael, R. D. 3 1937 Tactical configurations of rank two. JFM 57.0110.04Carmichael, R. D. 3 1931 Boundary value and expansion problems; formulation of various transcendental problems. JFM 48.0522.02Carmichael, R. D. 3 1921 Boundary value and expansion problems: oscillation, comparison and expansion theorems. JFM 48.0522.03Carmichael, R. D. 3 1922 History of the theory of numbers. JFM 47.0105.01Carmichael, R. D. 3 1920 Elementary inequations for the roots of an algebraic equations. JFM 46.0123.04Carmichael, R. D. 3 1918 On composite numbers \(P\) which satisfy the Fermat congruence \(a^{P-1}\equiv 1\) (mod. \(P\)). JFM 43.0276.17Carmichael, R. D. 3 1912 Summation of functions of a complex variable. Zbl 0006.40101Carmichael, R. D. 2 1933 On non-homogeneous linear differential equations of infinite order with constant coefficients. Zbl 0014.40205Carmichael, R. D. 2 1936 Linear differential equations of infinite order. JFM 62.0529.02Carmichael, R. D. 2 1936 On series of iterated linear fractional functions. JFM 45.0397.01Carmichael, R. D. 2 1914 On the numerical factors of the arithmetic forms \(\alpha^n\pm \beta^n\). (Abstract). JFM 44.0247.09Carmichael, R. D. 2 1913 Generalizations of Euler’s \(\varPhi\)-function, with applications to Abelian groups. JFM 43.0247.01Carmichael, R. D. 2 1912 The remainder term in a certain development of \(f(a+x)\). JFM 43.0529.04Carmichael, R. D. 2 1912 On \(r\)-fold svmmetry of plane algebraic curves. JFM 41.0653.03Carmichael, R. D. 2 1910 Multiply perfect numbers of four different primes. JFM 38.0235.01Carmichael, R. D. 2 1907 Mathematical tables and formulas. Zbl 0149.12803Carmichael, R. D.; Smith, E. R. 1 1962 Some recent researches in the theory of numbers. Zbl 0004.05304Carmichael, R. D. 1 1932 On a classification of integral functions by means of certain invariant point properties. Zbl 0016.03304Carmichael, R. D.; Martin, W. T.; Bird, M. T. 1 1936 Functions of exponential type. JFM 60.0263.02Carmichael, R. D. 1 1934 On expansions of arithmetical functions. JFM 56.0177.02Carmichael, R. D. 1 1930 The logic of discovery. JFM 56.0820.06Carmichael, R. D. 1 1930 A simple principle of unification in the elementary theory of numbers. JFM 55.0685.05Carmichael, R. D. 1 1929 The present state of the difference calculus and the prospect for the future. JFM 50.0318.02Carmichael, R. D. 1 1924 The present state of the difference calculus and the prospect for the future. JFM 50.0699.05Carmichael, R. D. 1 1924 Algebraic guides to transcendental problems. JFM 48.1253.02Carmichael, R. D. 1 1922 Modular systems. JFM 47.0100.03Carmichael, R. D. 1 1919 General aspects of the theory of summable series. JFM 47.0193.01Carmichael, R. D. 1 1918 On the solutions of linear homogeneous difference equations. JFM 46.0710.02Carmichael, R. D. 1 1916 On certain diophantine equations having multiple parameter solutions. JFM 45.0333.11Carmichael, R. D. 1 1913 On the representation of numbers in the form \(x^3 + y^3 + z^3 - 3xyz\). JFM 45.1251.04Carmichael, R. D. 1 1915 On transcendentally transcendental functions. JFM 44.0461.03Carmichael, R. D. 1 1913 The theory of relativity. JFM 44.0790.09Carmichael, R. D. 1 1913 A table of multiply perfect numbers. JFM 38.0235.02Carmichael, R. D. 1 1907 Mathematical tables and formulas. Zbl 0149.12803Carmichael, R. D.; Smith, E. R. 1 1962 The theory of numbers and Diophantine analysis. Unabridged and unaltered republ. of the latest ed. Zbl 0086.01104Carmichael, Robert D. 6 1959 Introduction to the theory of groups of finite order. 2nd edition. Zbl 0075.23901Carmichael, Robert D. 31 1956 Introduction to the theory of groups of finite order. Zbl 0019.19702Carmichael, R. D. 72 1937 Introduction to the theory of groups of finite order. JFM 63.0860.01Carmichael, R. D. 3 1937 Linear differential equations of infinite order. Zbl 0014.26004Carmichael, R. D. 10 1936 On non-homogeneous linear differential equations of infinite order with constant coefficients. Zbl 0014.40205Carmichael, R. D. 2 1936 Linear differential equations of infinite order. JFM 62.0529.02Carmichael, R. D. 2 1936 On a classification of integral functions by means of certain invariant point properties. Zbl 0016.03304Carmichael, R. D.; Martin, W. T.; Bird, M. T. 1 1936 Functions of exponential type. JFM 60.0263.02Carmichael, R. D. 1 1934 Systems of linear difference equations and expansions in series of exponential functions. Zbl 0006.16901Carmichael, R. D. 4 1933 Summation of functions of a complex variable. Zbl 0006.40101Carmichael, R. D. 2 1933 Expansions of arithmetical functions in infinite series. Zbl 0004.29305Carmichael, R. D. 13 1932 Expansions of arithmetical functions in infinite series. JFM 58.0184.01Carmichael, R. D. 5 1932 Some recent researches in the theory of numbers. Zbl 0004.05304Carmichael, R. D. 1 1932 Tactical configurations of rank two. Zbl 0001.01002Carmichael, R. D. 4 1931 Algebras of certain doubly transitive groups. Zbl 0002.01102Carmichael, R. D. 3 1931 Tactical configurations of rank two. JFM 57.0110.04Carmichael, R. D. 3 1931 On expansions of arithmetical functions. JFM 56.0177.02Carmichael, R. D. 1 1930 The logic of discovery. JFM 56.0820.06Carmichael, R. D. 1 1930 A simple principle of unification in the elementary theory of numbers. JFM 55.0685.05Carmichael, R. D. 1 1929 The present state of the difference calculus and the prospect for the future. JFM 50.0318.02Carmichael, R. D. 1 1924 The present state of the difference calculus and the prospect for the future. JFM 50.0699.05Carmichael, R. D. 1 1924 Note on Euler’s \(\varphi\)-function. JFM 48.0158.04Carmichael, R. D. 13 1922 Abstract definitions of the symmetric and alternating groups and certain other permutation groups. JFM 48.1148.03Carmichael, R. D. 7 1922 Boundary value and expansion problems: oscillation, comparison and expansion theorems. JFM 48.0522.03Carmichael, R. D. 3 1922 Algebraic guides to transcendental problems. JFM 48.1253.02Carmichael, R. D. 1 1922 Boundary value and expansion problems: algebraic basis of the theory. JFM 48.0522.01Carmichael, R. D. 6 1921 Boundary value and expansion problems; formulation of various transcendental problems. JFM 48.0522.02Carmichael, R. D. 3 1921 History of the theory of numbers. JFM 47.0105.01Carmichael, R. D. 3 1920 Modular systems. JFM 47.0100.03Carmichael, R. D. 1 1919 Elementary inequations for the roots of an algebraic equations. JFM 46.0123.04Carmichael, R. D. 3 1918 General aspects of the theory of summable series. JFM 47.0193.01Carmichael, R. D. 1 1918 On the solutions of linear homogeneous difference equations. JFM 46.0710.02Carmichael, R. D. 1 1916 Diophantine analysis. JFM 45.0283.11Carmichael, R. D. 8 1915 On the representation of numbers in the form \(x^3 + y^3 + z^3 - 3xyz\). JFM 45.1251.04Carmichael, R. D. 1 1915 On the numerical factors of the arithmetic forms \(\alpha^n\pm \beta^n\). JFM 45.1259.10Carmichael, R. D. 15 1914 Note on the roots of algebraic equations. JFM 45.0168.01Carmichael, R. D.; Mason, T. E. 13 1914 The theory of numbers. JFM 45.0283.10Carmichael, R. D. 9 1914 On series of iterated linear fractional functions. JFM 45.0397.01Carmichael, R. D. 2 1914 On the numerical factors of the arithmetic forms \(\alpha^n\pm \beta^n\). JFM 44.0216.01Carmichael, R. D. 94 1913 On the theory of linear difference equations. JFM 44.0397.03Carmichael, R. D. 6 1913 On the numerical factors of the arithmetic forms \(\alpha^n\pm \beta^n\). (Abstract). JFM 44.0247.09Carmichael, R. D. 2 1913 On certain diophantine equations having multiple parameter solutions. JFM 45.0333.11Carmichael, R. D. 1 1913 On transcendentally transcendental functions. JFM 44.0461.03Carmichael, R. D. 1 1913 The theory of relativity. JFM 44.0790.09Carmichael, R. D. 1 1913 The general theory of linear \(q\)-difference equations. JFM 43.0411.02Carmichael, R. D. 104 1912 On composite numbers \(P\) which satisfy the Fermat congruence \(a^{P-1}\equiv 1\) (mod. \(P\)). JFM 43.0276.17Carmichael, R. D. 3 1912 Generalizations of Euler’s \(\varPhi\)-function, with applications to Abelian groups. JFM 43.0247.01Carmichael, R. D. 2 1912 The remainder term in a certain development of \(f(a+x)\). JFM 43.0529.04Carmichael, R. D. 2 1912 Linear difference equations and their analytic solutions. JFM 42.0359.01Carmichael, R. D. 16 1911 On composite numbers \(P\) which satisfy the Fermat congruence \(a^{P-1}\equiv 1\pmod P\). JFM 42.0236.07Carmichael, R. D. 10 1911 Note on a new number theory function. JFM 41.0226.04Carmichael, R. D. 40 1910 On \(r\)-fold svmmetry of plane algebraic curves. JFM 41.0653.03Carmichael, R. D. 2 1910 On Euler’s \(\varphi\)-function. JFM 38.0236.01Carmichael, R. D. 9 1907 Multiply perfect numbers of four different primes. JFM 38.0235.01Carmichael, R. D. 2 1907 A table of multiply perfect numbers. JFM 38.0235.02Carmichael, R. D. 1 1907 all cited Publications top 5 cited Publications all top 5 Cited by 679 Authors 43 Luca, Florian 7 Sitthiwirattham, Thanin 7 Stănică, Pantelimon 6 Ntouyas, Sotiris K. 6 Samei, Mohammad Esmael 6 Somer, Lawrence E. 5 Abbas, Said 5 Ahmad, Bashir 5 Benchohra, Mouffak 5 Ingram, Patrick 5 Křížek, Michal 5 Pelyukh, Grygor P. 5 Pomerance, Carl Bernard 5 Tariboon, Jessada 5 Togbé, Alain 4 Bravo, Jhon Jairo 4 Faye, Bernadette 4 Gómez, Carlos Alexis 4 Guralnick, Robert Michael 4 Hamada, Noboru 4 Hamza, Alaa E. 4 Jones, Lenny K. 4 Joshi, Nalini 4 Kantor, William M. 4 Li, Shuguang 4 Patanarapeelert, Nichaphat 4 Trjitzinsky, Waldemar Joseph 4 Wright, Thomas 3 Alkan, Emre 3 Bennett, Michael A. 3 Darus, Maslina 3 Das, Bireswar 3 Datta, Biswa Tosh 3 Gulati, Bodh Raj 3 Ibrahim, Rabha Waell 3 Jarden, Moshe 3 Kageyama, Sanpei 3 Kassabov, Martin 3 Le, Maohua 3 Lubotzky, Alexander 3 Murty, Maruti Ram 3 Pollack, Paul 3 Rezapour, Shahram 3 Sharma, Shivdutt 3 Siksek, Samir 3 Silverman, Joseph Hillel 3 Sivak, Olena A. 3 Soontharanon, Jarunee 3 Voutier, Paul M. 3 Wang, Jufang 3 Yu, Changlong 2 Abdelkhaliq, Marwa M. 2 Abhyankar, Shreeram Shankar 2 Adegbindin, Chèfiath Awero 2 Al-saedi, Ahmed Eid Salem 2 Altintas, Osman 2 Anderson, Ian 2 Annaby, Mahmoud H. 2 Banks, William David 2 Binding, Paul Anthony 2 Boutiara, Abdelatif 2 Broughan, Kevin A. 2 Burton, Catherine T. 2 Cao, Tingbin 2 Chakravarti, Indra-Mohan 2 Chen, Haibo 2 Choudhry, Ajai 2 Cohen, Eckford 2 Cohen, Graeme L. 2 Ddamulira, Mahadi 2 Dembowski, Peter 2 Demirci, Musa 2 Dreyfus, Thomas 2 Dubickas, Artūras 2 Echi, Othman 2 Elobaid, Rafida M. 2 Etemad, Sina 2 Fiorenza, Alberto 2 Fried, Michael David 2 Gadiyar, Hejmadi Gopalakrishna 2 Ghanmi, Nejib 2 Ghermanesco, Michel 2 Graef, John R. 2 Grau, José María 2 Hanani, Haim 2 Hartman, Alan 2 Hedayati, Vahid 2 Hussain, Saqib 2 Irmak, Nurettin 2 Jamison, Robert E. 2 Kamsrisuk, Nattapong 2 Kang, Jung-Yoog 2 Kellner, Bernd C. 2 Khan, Shahid Ali 2 Kramer, Earl S. 2 Lagrange, René 2 Laledj, Nadjet 2 Lipshitz, Leonard 2 Liu, Zhi 2 Lü, Xiaodong ...and 579 more Authors all top 5 Cited in 195 Serials 29 Journal of Number Theory 20 Advances in Difference Equations 18 International Journal of Number Theory 16 Discrete Mathematics 12 Journal of Combinatorial Theory. Series A 12 Transactions of the American Mathematical Society 11 Mathematics of Computation 10 Journal of Mathematical Analysis and Applications 10 Czechoslovak Mathematical Journal 10 Journal of Algebra 9 Proceedings of the American Mathematical Society 8 Archiv der Mathematik 8 Mathematische Zeitschrift 8 Integers 7 Periodica Mathematica Hungarica 6 Bulletin of the Australian Mathematical Society 6 Turkish Journal of Mathematics 6 The Ramanujan Journal 5 Communications in Algebra 5 Acta Mathematica 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Mathematische Annalen 5 Monatshefte für Mathematik 5 Bulletin of the American Mathematical Society 5 AIMS Mathematics 4 Acta Arithmetica 4 Annales de l’Institut Fourier 4 Annals of the Institute of Statistical Mathematics 4 Journal of Pure and Applied Algebra 4 Theoretical Computer Science 4 Designs, Codes and Cryptography 4 Bulletin of the American Mathematical Society. New Series 4 Journal de Théorie des Nombres de Bordeaux 4 Journal of Function Spaces 3 Analysis Mathematica 3 Communications in Mathematical Physics 3 Journal of Mathematical Physics 3 Rocky Mountain Journal of Mathematics 3 Applied Mathematics and Computation 3 Computing 3 Duke Mathematical Journal 3 Functiones et Approximatio. Commentarii Mathematici 3 Journal of Computational and Applied Mathematics 3 Mathematica Slovaca 3 Mathematika 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 Linear Algebra and its Applications 3 Journal of Mathematical Sciences (New York) 3 Journal of Difference Equations and Applications 3 Discrete Dynamics in Nature and Society 3 Nonlinear Oscillations 3 Research in Number Theory 2 Acta Mathematica Academiae Scientiarum Hungaricae 2 American Mathematical Monthly 2 Discrete Applied Mathematics 2 International Journal of Control 2 The Mathematical Gazette 2 Mathematical Notes 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Ukrainian Mathematical Journal 2 Arkiv för Matematik 2 The Mathematical Intelligencer 2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2 Bulletin of the London Mathematical Society 2 Journal of Computer and System Sciences 2 Journal für die Reine und Angewandte Mathematik 2 Journal of Statistical Planning and Inference 2 Nagoya Mathematical Journal 2 Proceedings of the Japan Academy. Series A 2 Publications de l’Institut Mathématique. Nouvelle Série 2 Quaestiones Mathematicae 2 Rendiconti del Seminario Matematico della Università di Padova 2 Results in Mathematics 2 European Journal of Combinatorics 2 Journal of the American Mathematical Society 2 Aequationes Mathematicae 2 Indagationes Mathematicae. New Series 2 Filomat 2 Finite Fields and their Applications 2 Journal of Combinatorial Designs 2 Journal of Inequalities and Applications 2 Journal of the European Mathematical Society (JEMS) 2 Communications of the Korean Mathematical Society 2 Mathematical Modelling and Analysis 2 Journal of the Australian Mathematical Society 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Boundary Value Problems 2 Science China. Mathematics 2 Annales Mathématiques du Québec 1 Archive for History of Exact Sciences 1 Classical and Quantum Gravity 1 Houston Journal of Mathematics 1 International Journal of Mathematical Education in Science and Technology 1 Indian Journal of Pure & Applied Mathematics 1 Information Processing Letters 1 Israel Journal of Mathematics 1 Journal of the Franklin Institute 1 Journal of Statistical Physics 1 Letters in Mathematical Physics 1 Lithuanian Mathematical Journal ...and 95 more Serials all top 5 Cited in 48 Fields 229 Number theory (11-XX) 83 Difference and functional equations (39-XX) 79 Combinatorics (05-XX) 54 Group theory and generalizations (20-XX) 37 Ordinary differential equations (34-XX) 28 Functions of a complex variable (30-XX) 23 Real functions (26-XX) 21 Information and communication theory, circuits (94-XX) 19 Algebraic geometry (14-XX) 19 Geometry (51-XX) 18 Field theory and polynomials (12-XX) 18 Special functions (33-XX) 15 Computer science (68-XX) 14 Operator theory (47-XX) 10 Numerical analysis (65-XX) 9 Statistics (62-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 8 Dynamical systems and ergodic theory (37-XX) 6 History and biography (01-XX) 6 Mathematical logic and foundations (03-XX) 6 Quantum theory (81-XX) 5 Associative rings and algebras (16-XX) 5 Nonassociative rings and algebras (17-XX) 5 Integral equations (45-XX) 5 Functional analysis (46-XX) 4 Partial differential equations (35-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Integral transforms, operational calculus (44-XX) 4 Systems theory; control (93-XX) 3 Approximations and expansions (41-XX) 3 Convex and discrete geometry (52-XX) 3 Manifolds and cell complexes (57-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Relativity and gravitational theory (83-XX) 3 Operations research, mathematical programming (90-XX) 2 General and overarching topics; collections (00-XX) 2 Commutative algebra (13-XX) 2 Category theory; homological algebra (18-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Sequences, series, summability (40-XX) 2 Algebraic topology (55-XX) 2 Biology and other natural sciences (92-XX) 1 \(K\)-theory (19-XX) 1 Abstract harmonic analysis (43-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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