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Carmichael, Robert D.

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Author ID: carmichael.robert-d Recent zbMATH articles by "Carmichael, Robert D."
Published as: Carmichael, R. D.; Carmichael, Robert D.
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Documents Indexed: 176 Publications since 1906, including 17 Books

Publications by Year

Citations contained in zbMATH Open

56 Publications have been cited 491 times in 436 Documents Cited by Year
On the numerical factors of the arithmetic forms \(\alpha^n\pm \beta^n\). JFM 44.0216.01
Carmichael, R. D.
82
1913
Introduction to the theory of groups of finite order. Zbl 0019.19702
Carmichael, R. D.
74
1937
The general theory of linear \(q\)-difference equations. JFM 43.0411.02
Carmichael, R. D.
64
1912
Introduction to the theory of groups of finite order. 2nd edition. Zbl 0075.23901
Carmichael, Robert D.
46
1956
Note on a new number theory function. JFM 41.0226.04
Carmichael, R. D.
34
1910
Linear difference equations and their analytic solutions. JFM 42.0359.01
Carmichael, R. D.
15
1911
On the numerical factors of the arithmetic forms \(\alpha^n\pm \beta^n\). JFM 45.1259.10
Carmichael, R. D.
13
1914
Expansions of arithmetical functions in infinite series. Zbl 0004.29305
Carmichael, R. D.
12
1932
Note on Euler’s \(\varphi\)-function. JFM 48.0158.04
Carmichael, R. D.
11
1922
The theory of numbers. JFM 45.0283.10
Carmichael, R. D.
11
1914
Linear differential equations of infinite order. Zbl 0014.26004
Carmichael, R. D.
10
1936
Note on the roots of algebraic equations. JFM 45.0168.01
Carmichael, R. D.; Mason, T. E.
10
1914
On Euler’s \(\varphi\)-function. JFM 38.0236.01
Carmichael, R. D.
8
1907
The theory of numbers and Diophantine analysis. Unabridged and unaltered republ. of the latest ed. Zbl 0086.01104
Carmichael, Robert D.
7
1959
Abstract definitions of the symmetric and alternating groups and certain other permutation groups. JFM 48.1148.03
Carmichael, R. D.
7
1922
Diophantine analysis. JFM 45.0283.11
Carmichael, R. D.
7
1915
On the theory of linear difference equations. JFM 44.0397.03
Carmichael, R. D.
6
1913
On composite numbers \(P\) which satisfy the Fermat congruence \(a^{P-1}\equiv 1\pmod P\). JFM 42.0236.07
Carmichael, R. D.
6
1911
Systems of linear difference equations and expansions in series of exponential functions. Zbl 0006.16901
Carmichael, R. D.
4
1933
Tactical configurations of rank two. Zbl 0001.01002
Carmichael, R. D.
4
1931
Boundary value and expansion problems: algebraic basis of the theory. JFM 48.0522.01
Carmichael, R. D.
4
1921
Expansions of arithmetical functions in infinite series. JFM 58.0184.01
Carmichael, R. D.
3
1932
Algebras of certain doubly transitive groups. Zbl 0002.01102
Carmichael, R. D.
3
1931
History of the theory of numbers. JFM 47.0105.01
Carmichael, R. D.
3
1920
Elementary inequations for the roots of an algebraic equations. JFM 46.0123.04
Carmichael, R. D.
3
1918
On composite numbers \(P\) which satisfy the Fermat congruence \(a^{P-1}\equiv 1\) (mod. \(P\)). JFM 43.0276.17
Carmichael, R. D.
3
1912
On non-homogeneous linear differential equations of infinite order with constant coefficients. Zbl 0014.40205
Carmichael, R. D.
2
1936
Linear differential equations of infinite order. JFM 62.0529.02
Carmichael, R. D.
2
1936
Summation of functions of a complex variable. Zbl 0006.40101
Carmichael, R. D.
2
1933
Tactical configurations of rank two. JFM 57.0110.04
Carmichael, R. D.
2
1931
Boundary value and expansion problems: oscillation, comparison and expansion theorems. JFM 48.0522.03
Carmichael, R. D.
2
1922
Boundary value and expansion problems; formulation of various transcendental problems. JFM 48.0522.02
Carmichael, R. D.
2
1921
On series of iterated linear fractional functions. JFM 45.0397.01
Carmichael, R. D.
2
1914
The remainder term in a certain development of \(f(a+x)\). JFM 43.0529.04
Carmichael, R. D.
2
1912
Generalizations of Euler’s \(\varPhi\)-function, with applications to Abelian groups. JFM 43.0247.01
Carmichael, R. D.
2
1912
On \(r\)-fold svmmetry of plane algebraic curves. JFM 41.0653.03
Carmichael, R. D.
2
1910
Multiply perfect numbers of four different primes. JFM 38.0235.01
Carmichael, R. D.
2
1907
Mathematical tables and formulas. Zbl 0149.12803
Carmichael, R. D.; Smith, E. R.
1
1962
On a classification of integral functions by means of certain invariant point properties. Zbl 0016.03304
Carmichael, R. D.; Martin, W. T.; Bird, M. T.
1
1936
Functions of exponential type. JFM 60.0263.02
Carmichael, R. D.
1
1934
Some recent researches in the theory of numbers. Zbl 0004.05304
Carmichael, R. D.
1
1932
The logic of discovery. JFM 56.0820.06
Carmichael, R. D.
1
1930
On expansions of arithmetical functions. JFM 56.0177.02
Carmichael, R. D.
1
1930
A simple principle of unification in the elementary theory of numbers. JFM 55.0685.05
Carmichael, R. D.
1
1929
Transformations leaving invariant certain partial differential equation of physics. JFM 53.0396.05
Carmichael, R. D.
1
1927
The present state of the difference calculus and the prospect for the future. JFM 50.0699.05
Carmichael, R. D.
1
1924
Algebraic guides to transcendental problems. JFM 48.1253.02
Carmichael, R. D.
1
1922
Modular systems. JFM 47.0100.03
Carmichael, R. D.
1
1919
General aspects of the theory of summable series. JFM 47.0193.01
Carmichael, R. D.
1
1918
On the solutions of linear homogeneous difference equations. JFM 46.0710.02
Carmichael, R. D.
1
1916
On the representation of numbers in the form \(x^3 + y^3 + z^3 - 3xyz\). JFM 45.1251.04
Carmichael, R. D.
1
1915
The theory of relativity. JFM 44.0790.09
Carmichael, R. D.
1
1913
On transcendentally transcendental functions. JFM 44.0461.03
Carmichael, R. D.
1
1913
On the numerical factors of the arithmetic forms \(\alpha^n\pm \beta^n\). (Abstract). JFM 44.0247.09
Carmichael, R. D.
1
1913
On certain diophantine equations having multiple parameter solutions. JFM 45.0333.11
Carmichael, R. D.
1
1913
A table of multiply perfect numbers. JFM 38.0235.02
Carmichael, R. D.
1
1907
Mathematical tables and formulas. Zbl 0149.12803
Carmichael, R. D.; Smith, E. R.
1
1962
The theory of numbers and Diophantine analysis. Unabridged and unaltered republ. of the latest ed. Zbl 0086.01104
Carmichael, Robert D.
7
1959
Introduction to the theory of groups of finite order. 2nd edition. Zbl 0075.23901
Carmichael, Robert D.
46
1956
Introduction to the theory of groups of finite order. Zbl 0019.19702
Carmichael, R. D.
74
1937
Linear differential equations of infinite order. Zbl 0014.26004
Carmichael, R. D.
10
1936
On non-homogeneous linear differential equations of infinite order with constant coefficients. Zbl 0014.40205
Carmichael, R. D.
2
1936
Linear differential equations of infinite order. JFM 62.0529.02
Carmichael, R. D.
2
1936
On a classification of integral functions by means of certain invariant point properties. Zbl 0016.03304
Carmichael, R. D.; Martin, W. T.; Bird, M. T.
1
1936
Functions of exponential type. JFM 60.0263.02
Carmichael, R. D.
1
1934
Systems of linear difference equations and expansions in series of exponential functions. Zbl 0006.16901
Carmichael, R. D.
4
1933
Summation of functions of a complex variable. Zbl 0006.40101
Carmichael, R. D.
2
1933
Expansions of arithmetical functions in infinite series. Zbl 0004.29305
Carmichael, R. D.
12
1932
Expansions of arithmetical functions in infinite series. JFM 58.0184.01
Carmichael, R. D.
3
1932
Some recent researches in the theory of numbers. Zbl 0004.05304
Carmichael, R. D.
1
1932
Tactical configurations of rank two. Zbl 0001.01002
Carmichael, R. D.
4
1931
Algebras of certain doubly transitive groups. Zbl 0002.01102
Carmichael, R. D.
3
1931
Tactical configurations of rank two. JFM 57.0110.04
Carmichael, R. D.
2
1931
The logic of discovery. JFM 56.0820.06
Carmichael, R. D.
1
1930
On expansions of arithmetical functions. JFM 56.0177.02
Carmichael, R. D.
1
1930
A simple principle of unification in the elementary theory of numbers. JFM 55.0685.05
Carmichael, R. D.
1
1929
Transformations leaving invariant certain partial differential equation of physics. JFM 53.0396.05
Carmichael, R. D.
1
1927
The present state of the difference calculus and the prospect for the future. JFM 50.0699.05
Carmichael, R. D.
1
1924
Note on Euler’s \(\varphi\)-function. JFM 48.0158.04
Carmichael, R. D.
11
1922
Abstract definitions of the symmetric and alternating groups and certain other permutation groups. JFM 48.1148.03
Carmichael, R. D.
7
1922
Boundary value and expansion problems: oscillation, comparison and expansion theorems. JFM 48.0522.03
Carmichael, R. D.
2
1922
Algebraic guides to transcendental problems. JFM 48.1253.02
Carmichael, R. D.
1
1922
Boundary value and expansion problems: algebraic basis of the theory. JFM 48.0522.01
Carmichael, R. D.
4
1921
Boundary value and expansion problems; formulation of various transcendental problems. JFM 48.0522.02
Carmichael, R. D.
2
1921
History of the theory of numbers. JFM 47.0105.01
Carmichael, R. D.
3
1920
Modular systems. JFM 47.0100.03
Carmichael, R. D.
1
1919
Elementary inequations for the roots of an algebraic equations. JFM 46.0123.04
Carmichael, R. D.
3
1918
General aspects of the theory of summable series. JFM 47.0193.01
Carmichael, R. D.
1
1918
On the solutions of linear homogeneous difference equations. JFM 46.0710.02
Carmichael, R. D.
1
1916
Diophantine analysis. JFM 45.0283.11
Carmichael, R. D.
7
1915
On the representation of numbers in the form \(x^3 + y^3 + z^3 - 3xyz\). JFM 45.1251.04
Carmichael, R. D.
1
1915
On the numerical factors of the arithmetic forms \(\alpha^n\pm \beta^n\). JFM 45.1259.10
Carmichael, R. D.
13
1914
The theory of numbers. JFM 45.0283.10
Carmichael, R. D.
11
1914
Note on the roots of algebraic equations. JFM 45.0168.01
Carmichael, R. D.; Mason, T. E.
10
1914
On series of iterated linear fractional functions. JFM 45.0397.01
Carmichael, R. D.
2
1914
On the numerical factors of the arithmetic forms \(\alpha^n\pm \beta^n\). JFM 44.0216.01
Carmichael, R. D.
82
1913
On the theory of linear difference equations. JFM 44.0397.03
Carmichael, R. D.
6
1913
The theory of relativity. JFM 44.0790.09
Carmichael, R. D.
1
1913
On transcendentally transcendental functions. JFM 44.0461.03
Carmichael, R. D.
1
1913
On the numerical factors of the arithmetic forms \(\alpha^n\pm \beta^n\). (Abstract). JFM 44.0247.09
Carmichael, R. D.
1
1913
On certain diophantine equations having multiple parameter solutions. JFM 45.0333.11
Carmichael, R. D.
1
1913
The general theory of linear \(q\)-difference equations. JFM 43.0411.02
Carmichael, R. D.
64
1912
On composite numbers \(P\) which satisfy the Fermat congruence \(a^{P-1}\equiv 1\) (mod. \(P\)). JFM 43.0276.17
Carmichael, R. D.
3
1912
The remainder term in a certain development of \(f(a+x)\). JFM 43.0529.04
Carmichael, R. D.
2
1912
Generalizations of Euler’s \(\varPhi\)-function, with applications to Abelian groups. JFM 43.0247.01
Carmichael, R. D.
2
1912
Linear difference equations and their analytic solutions. JFM 42.0359.01
Carmichael, R. D.
15
1911
On composite numbers \(P\) which satisfy the Fermat congruence \(a^{P-1}\equiv 1\pmod P\). JFM 42.0236.07
Carmichael, R. D.
6
1911
Note on a new number theory function. JFM 41.0226.04
Carmichael, R. D.
34
1910
On \(r\)-fold svmmetry of plane algebraic curves. JFM 41.0653.03
Carmichael, R. D.
2
1910
On Euler’s \(\varphi\)-function. JFM 38.0236.01
Carmichael, R. D.
8
1907
Multiply perfect numbers of four different primes. JFM 38.0235.01
Carmichael, R. D.
2
1907
A table of multiply perfect numbers. JFM 38.0235.02
Carmichael, R. D.
1
1907
all top 5

Cited by 575 Authors

39 Luca, Florian
7 Stănică, Pantelimon
6 Somer, Lawrence E.
5 Ingram, Patrick
5 Křížek, Michal
5 Tariboon, Jessada
4 Guralnick, Robert Michael
4 Hamada, Noboru
4 Hamza, Alaa E.
4 Jones, Lenny K.
4 Kantor, William M.
4 Li, Shuguang
4 Ntouyas, Sotiris K.
4 Trjitzinsky, Waldemar Joseph
4 Wright, Thomas
3 Ahmad, Bashir
3 Alkan, Emre
3 Bravo, Jhon Jairo
3 Datta, Biswa Tosh
3 Faye, Bernadette
3 Gómez Ruiz, Carlos Alexis
3 Gulati, Bodh Raj
3 Jarden, Moshe
3 Joshi, Nalini
3 Kageyama, Sanpei
3 Kassabov, Martin
3 Lubotzky, Alexander
3 Murty, Maruti Ram
3 Pelyukh, H. P.
3 Pollack, Paul
3 Pomerance, Carl Bernard
3 Silverman, Joseph Hillel
3 Sivak, Olena A.
3 Togbé, Alain
3 Voutier, Paul M.
3 Vsemirnov, Maxim
3 Wang, Jufang
3 Yu, Changlong
2 Abdelkhaliq, Marwa M.
2 Abhyankar, Shreeram Shankar
2 Al-saedi, Ahmed Eid Salem
2 Anderson, Ian
2 Annaby, Mahmoud H.
2 Banks, William D.
2 Binding, Paul Anthony
2 Broughan, Kevin A.
2 Burton, Catherine T.
2 Chakravarti, Indra-Mohan
2 Chen, Haibo
2 Cohen, Eckford
2 Cohen, Graeme L.
2 Dembowski, Peter
2 Dreyfus, Thomas
2 Dubickas, Artūras
2 Echi, Othman
2 Fried, Michael David
2 Gadiyar, Hejmadi Gopalakrishna
2 Ghermanesco, Michel
2 Grau, José María
2 Hanani, Haim
2 Hartman, Alan
2 Irmak, Nurettin
2 Jamison, Robert E.
2 Kamsrisuk, Nattapong
2 Kang, Jung-Yoog
2 Kramer, Earl S.
2 Lagrange, René
2 Le, Maohua
2 Lipshitz, Leonard
2 Liu, Zhi
2 Lü, Xiaodong
2 Lucht, Lutz Gerhard
2 Matala-aho, Tapani
2 Meemark, Yotsanan
2 Mejri, Manoubi
2 Mimachi, Katsuhisa
2 Najman, Filip
2 Niemeyer, Alice C.
2 Nieto Roig, Juan Jose
2 Oller-Marcén, Antonio M.
2 Padma, Ramanathan
2 Patanarapeelert, Nichaphat
2 Pelyukh, Grygor P.
2 Phelps, Kevin T.
2 Prado, Humberto E.
2 Preece, Donald Arthur
2 Prévost, Marc
2 Promsakon, Chanon
2 Řehák, Pavel
2 Reshetikhin, Nikolai Yu.
2 Reyes, Enrique G.
2 Rosa, Alexander
2 Rouse, Jeremy A.
2 Rout, Sudhansu Sekhar
2 Sanchez, Sergio Guzman
2 Si, Jianguo
2 Singer, Michael F.
2 Sitthiwirattham, Thanin
2 Skowronek-Kaziów, Joanna
2 Soydan, Gokhan
...and 475 more Authors
all top 5

Cited in 166 Serials

29 Journal of Number Theory
16 Discrete Mathematics
14 International Journal of Number Theory
13 Journal of Combinatorial Theory. Series A
11 Mathematics of Computation
11 Transactions of the American Mathematical Society
10 Journal of Mathematical Analysis and Applications
10 Czechoslovak Mathematical Journal
10 Journal of Algebra
9 Proceedings of the American Mathematical Society
9 Advances in Difference Equations
8 Archiv der Mathematik
8 Mathematische Zeitschrift
6 Annali di Matematica Pura ed Applicata. Serie Quarta
6 Integers
5 Bulletin of the Australian Mathematical Society
5 Communications in Algebra
5 Periodica Mathematica Hungarica
5 Acta Mathematica
5 Monatshefte für Mathematik
5 Bulletin of the American Mathematical Society
4 Acta Arithmetica
4 Annals of the Institute of Statistical Mathematics
4 Journal of Pure and Applied Algebra
4 Mathematische Annalen
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 The Ramanujan Journal
3 Communications in Mathematical Physics
3 Rocky Mountain Journal of Mathematics
3 Annales de l’Institut Fourier
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 Mathematika
3 Proceedings of the Edinburgh Mathematical Society. Series II
3 Linear Algebra and its Applications
3 Journal of Difference Equations and Applications
3 Discrete Dynamics in Nature and Society
3 Nonlinear Oscillations
2 Acta Mathematica Academiae Scientiarum Hungaricae
2 Discrete Applied Mathematics
2 International Journal of Control
2 Journal of Mathematical Physics
2 The Mathematical Gazette
2 Mathematical Notes
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 Information Sciences
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 Rendiconti del Seminario Matematico della Università di Padova
2 Results in Mathematics
2 European Journal of Combinatorics
2 Annals of Pure and Applied Logic
2 Journal of the American Mathematical Society
2 Aequationes Mathematicae
2 Indagationes Mathematicae. New Series
2 Journal of Mathematical Sciences (New York)
2 Journal of Combinatorial Designs
2 Journal of the European Mathematical Society (JEMS)
2 Communications of the Korean Mathematical Society
2 Journal of High Energy Physics
2 Journal of the Australian Mathematical Society
2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
2 Science China. Mathematics
2 Annales Mathématiques du Québec
2 Journal of Function Spaces
1 American Mathematical Monthly
1 Analysis Mathematica
1 Archive for History of Exact Sciences
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
1 Mathematical Proceedings of the Cambridge Philosophical Society
1 Reports on Mathematical Physics
1 Mathematics Magazine
1 BIT
1 Glasgow Mathematical Journal
1 International Journal of Mathematics and Mathematical Sciences
1 Journal of Combinatorial Theory. Series B
1 Journal of Differential Equations
1 Journal of Geometry
1 Journal of Optimization Theory and Applications
...and 66 more Serials
all top 5

Cited in 47 Fields

191 Number theory (11-XX)
70 Combinatorics (05-XX)
57 Difference and functional equations (39-XX)
48 Group theory and generalizations (20-XX)
24 Ordinary differential equations (34-XX)
21 Geometry (51-XX)
20 Information and communication theory, circuits (94-XX)
17 Special functions (33-XX)
16 Field theory and polynomials (12-XX)
16 Algebraic geometry (14-XX)
14 Functions of a complex variable (30-XX)
13 Computer science (68-XX)
9 Operator theory (47-XX)
9 Statistics (62-XX)
8 Numerical analysis (65-XX)
7 Mathematical logic and foundations (03-XX)
7 Quantum theory (81-XX)
6 History and biography (01-XX)
6 Linear and multilinear algebra; matrix theory (15-XX)
5 Real functions (26-XX)
5 Dynamical systems and ergodic theory (37-XX)
4 Associative rings and algebras (16-XX)
4 Nonassociative rings and algebras (17-XX)
4 Systems theory; control (93-XX)
3 Partial differential equations (35-XX)
3 Harmonic analysis on Euclidean spaces (42-XX)
3 Integral transforms, operational calculus (44-XX)
3 Functional analysis (46-XX)
3 Manifolds and cell complexes (57-XX)
3 Statistical mechanics, structure of matter (82-XX)
3 Relativity and gravitational theory (83-XX)
2 Sequences, series, summability (40-XX)
2 Approximations and expansions (41-XX)
2 Convex and discrete geometry (52-XX)
2 Operations research, mathematical programming (90-XX)
2 Biology and other natural sciences (92-XX)
1 General and overarching topics; collections (00-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 General algebraic systems (08-XX)
1 Commutative algebra (13-XX)
1 Category theory; homological algebra (18-XX)
1 \(K\)-theory (19-XX)
1 Abstract harmonic analysis (43-XX)
1 Integral equations (45-XX)
1 Algebraic topology (55-XX)
1 Probability theory and stochastic processes (60-XX)
1 Mathematics education (97-XX)

Citations by Year

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