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Author ID: rosen.michael-i Recent zbMATH articles by "Rosen, Michael I."
Published as: Rosen, Michael; Rosen, Michael I.; Rosen, M.; Rosen, M. I.
Homepage: http://www.math.brown.edu/faculty/rosen.html
External Links: MGP · Wikidata · GND · IdRef

Publications by Year

Citations contained in zbMATH Open

56 Publications have been cited 1,881 times in 1,746 Documents Cited by Year
A classical introduction to modern number theory. 2nd ed. Zbl 0712.11001
Ireland, Kenneth; Rosen, Michael
718
1990
Number theory in function fields. Zbl 1043.11079
Rosen, Michael
372
2002
A classical introduction to modern number theory. (Rev. and expand. version of 1972). Zbl 0482.10001
Ireland, Kenneth; Rosen, Michael
246
1982
Idempotent relations and factors of Jacobians. Zbl 0652.14011
Kani, E.; Rosen, M.
69
1989
The Hilbert class field in function fields. Zbl 0632.12017
Rosen, Michael
47
1987
Average values of L-series in function fields. Zbl 0754.11036
Hoffstein, Jeffrey; Rosen, Michael
37
1992
A generalization of Mertens’ theorem. Zbl 1133.11317
Rosen, Michael
33
1999
Units and class groups in cyclotomic function fields. Zbl 0483.12003
Galovich, Steven; Rosen, Michael
28
1982
\(S\)-units and \(S\)-class group in algebraic function fields. Zbl 0265.12003
Rosen, Michael
27
1973
The class number of cyclotomic function fields. Zbl 0473.12014
Galovich, Steven; Rosen, Michael
26
1981
Elements of number theory including an introduction to equations over finite fields. Zbl 0248.10002
Ireland, Kenneth; Rosen, Michael I.
21
1972
Ambiguous divisor classes in function fields. Zbl 0371.12013
Rosen, Michael
17
1977
On the rank of an elliptic surface. Zbl 0905.14019
Rosen, Michael; Silverman, Joseph H.
16
1998
The norm map for ordinary Abelian varieties. Zbl 0417.14035
Lubin, Jonathan; Rosen, Michael I.
16
1978
Group-theoretic constraints on the structure of the class group. Zbl 0456.12005
Cornell, Gary; Rosen, Michael
13
1981
Class number and ramification in number fields. Zbl 0128.26204
Brumer, Armand; Rosen, Michael
11
1963
On the independence of Heegner points associated to distinct quadratic imaginary fields. Zbl 1151.11024
Rosen, Michael; Silverman, Joseph H.
10
2007
Abel’s theorem on the lemniscate. Zbl 0491.14023
Rosen, Michael
10
1981
Variations on a theme of Romanoff. Zbl 0869.11004
Murty, M. Ram; Rosen, Michael; Silverman, Joseph H.
10
1996
An upper bound for the conductor of an abelian variety. Zbl 0816.14021
Lockhart, Paul; Rosen, Michael; Silverman, Joseph H.
10
1993
Fourier series and the special values of \(L\)-functions. Zbl 0649.12009
Gross, Benedict; Rosen, Michael
9
1988
A proof of the Lucas-Lehmer test. Zbl 0669.10015
Rosen, Michael I.
9
1988
Some remarks on the p-rank of an algebraic curve. Zbl 0524.14025
Rosen, Michael
8
1983
Formal Drinfeld modules. Zbl 1049.11060
Rosen, Michael
8
2003
Idempotent relations among arithmetic invariants attached to number fields and algebraic varieties. Zbl 0853.14011
Kani, Ernst; Rosen, Michael
8
1994
Number theory in function fields. Zbl 0830.11044
Rosen, Michael
7
1994
Average value of class numbers in cyclic extensions of the rational function field. Zbl 0839.11059
Rosen, Michael
7
1995
Two theorems on Galois cohomology. Zbl 0147.04001
Rosen, Michael
7
1966
The asymptotic behavior of the class group of a function field over a finite field. Zbl 0264.12003
Rosen, Michael
7
1973
Distributions on rational function fields. Zbl 0472.12013
Galovich, Steven; Rosen, Michael
6
1981
The St. Petersburg School of Number Theory. Transl. from the Russian by Robert Burns. Zbl 1074.11002
Delone, B. N.
6
2005
A note on the relative class number in function fields. Zbl 0872.11045
Rosen, Michael
6
1997
The \(\ell\)-rank of the real class group of cyclotomic fields. Zbl 0551.12006
Cornell, Gary; Rosen, Michael I.
5
1984
On the size of the Brauer group. Zbl 0182.07602
Brumer, A.; Rosen, M.
5
1968
A note on the splitting of the Hilbert class field. Zbl 0633.12003
Cornell, Gary; Rosen, Michael
4
1988
The class group of an absolutely abelian \(\ell\)-extension. Zbl 0654.12006
Cornell, Gary; Rosen, Michael
4
1988
The rank of abelian varieties over infinite Galois extensions. Zbl 1001.11025
Rosen, Michael; Wong, Siman
4
2002
The Jacobson radical of a group algebra. Zbl 0151.02205
Rosen, M. I.
4
1966
The automorphism group of a function field. Zbl 0791.14011
Madan, Manohar; Rosen, Michael
4
1992
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.) Zbl 0662.10001
Ireland, Kenneth F.; Rosen, Michael I.
3
1987
Torsion points of generic formal groups. Zbl 0669.14011
Rosen, Michael; Zimmermann, Karl
3
1989
Niels Hendrik Abel and equations of the fifth degree. Zbl 0836.01015
Rosen, Michael I.
3
1995
Function fields with class number indivisible by a prime \(\ell \). Zbl 1263.11098
Daub, Michael; Lang, Jaclyn; Merling, Mona; Pacelli, Allison M.; Pitiwan, Natee; Rosen, Michael
3
2011
An elementary proof of the local Kronecker-Weber theorem. Zbl 0474.12014
Rosen, Michael
3
1981
Direct products of cyclic groups. Zbl 0136.28501
Rosen, M.
3
1966
Average value of \(| K_ 2({\mathcal O})|\) in function fields. Zbl 0828.11069
Rosen, Michael
2
1995
The arithmetic of function fields. Proceedings of the workshop at the Ohio State University, June 17-26, 1991, Columbus, Ohio (USA). Zbl 0771.00031
2
1992
Class groups in cyclic \(\ell \)-extensions: comments on a paper by G. Cornell. Zbl 1329.11119
Rosen, Michael
2
2014
Elliptic curves and Dedekind domains. Zbl 0337.13014
Rosen, Michael
1
1976
Cohomological analysis of the class group extension problem. Zbl 0471.12012
Cornell, Gary; Rosen, M.
1
1980
Indivisibility of class numbers of global function fields. Zbl 1242.11094
Pacelli, Allison M.; Rosen, Michael
1
2009
Abelian varieties over \({\mathbb{C}}.\) (Notes by F. O. McGuinness). Zbl 0604.14032
Rosen, Michael
1
1986
Some confirming instances of the Birch-Swinnerton-Dyer conjecture over biquadratic fields. Zbl 0754.14013
Rosen, Michael I.
1
1990
Remarks on the history of Fermat’s Last Theorem 1844 to 1984. Zbl 0893.11011
Rosen, Michael
1
1997
Eisenstein reciprocity and \(n\)th-power residues. Zbl 0458.10002
Kraft, James; Rosen, Michael
1
1981
Polynomials modulo \(p\) and the theory of Galois sets. Zbl 1298.11025
Rosen, Michael
1
2012
Class groups in cyclic \(\ell \)-extensions: comments on a paper by G. Cornell. Zbl 1329.11119
Rosen, Michael
2
2014
Polynomials modulo \(p\) and the theory of Galois sets. Zbl 1298.11025
Rosen, Michael
1
2012
Function fields with class number indivisible by a prime \(\ell \). Zbl 1263.11098
Daub, Michael; Lang, Jaclyn; Merling, Mona; Pacelli, Allison M.; Pitiwan, Natee; Rosen, Michael
3
2011
Indivisibility of class numbers of global function fields. Zbl 1242.11094
Pacelli, Allison M.; Rosen, Michael
1
2009
On the independence of Heegner points associated to distinct quadratic imaginary fields. Zbl 1151.11024
Rosen, Michael; Silverman, Joseph H.
10
2007
The St. Petersburg School of Number Theory. Transl. from the Russian by Robert Burns. Zbl 1074.11002
Delone, B. N.
6
2005
Formal Drinfeld modules. Zbl 1049.11060
Rosen, Michael
8
2003
Number theory in function fields. Zbl 1043.11079
Rosen, Michael
372
2002
The rank of abelian varieties over infinite Galois extensions. Zbl 1001.11025
Rosen, Michael; Wong, Siman
4
2002
A generalization of Mertens’ theorem. Zbl 1133.11317
Rosen, Michael
33
1999
On the rank of an elliptic surface. Zbl 0905.14019
Rosen, Michael; Silverman, Joseph H.
16
1998
A note on the relative class number in function fields. Zbl 0872.11045
Rosen, Michael
6
1997
Remarks on the history of Fermat’s Last Theorem 1844 to 1984. Zbl 0893.11011
Rosen, Michael
1
1997
Variations on a theme of Romanoff. Zbl 0869.11004
Murty, M. Ram; Rosen, Michael; Silverman, Joseph H.
10
1996
Average value of class numbers in cyclic extensions of the rational function field. Zbl 0839.11059
Rosen, Michael
7
1995
Niels Hendrik Abel and equations of the fifth degree. Zbl 0836.01015
Rosen, Michael I.
3
1995
Average value of \(| K_ 2({\mathcal O})|\) in function fields. Zbl 0828.11069
Rosen, Michael
2
1995
Idempotent relations among arithmetic invariants attached to number fields and algebraic varieties. Zbl 0853.14011
Kani, Ernst; Rosen, Michael
8
1994
Number theory in function fields. Zbl 0830.11044
Rosen, Michael
7
1994
An upper bound for the conductor of an abelian variety. Zbl 0816.14021
Lockhart, Paul; Rosen, Michael; Silverman, Joseph H.
10
1993
Average values of L-series in function fields. Zbl 0754.11036
Hoffstein, Jeffrey; Rosen, Michael
37
1992
The automorphism group of a function field. Zbl 0791.14011
Madan, Manohar; Rosen, Michael
4
1992
The arithmetic of function fields. Proceedings of the workshop at the Ohio State University, June 17-26, 1991, Columbus, Ohio (USA). Zbl 0771.00031
2
1992
A classical introduction to modern number theory. 2nd ed. Zbl 0712.11001
Ireland, Kenneth; Rosen, Michael
718
1990
Some confirming instances of the Birch-Swinnerton-Dyer conjecture over biquadratic fields. Zbl 0754.14013
Rosen, Michael I.
1
1990
Idempotent relations and factors of Jacobians. Zbl 0652.14011
Kani, E.; Rosen, M.
69
1989
Torsion points of generic formal groups. Zbl 0669.14011
Rosen, Michael; Zimmermann, Karl
3
1989
Fourier series and the special values of \(L\)-functions. Zbl 0649.12009
Gross, Benedict; Rosen, Michael
9
1988
A proof of the Lucas-Lehmer test. Zbl 0669.10015
Rosen, Michael I.
9
1988
A note on the splitting of the Hilbert class field. Zbl 0633.12003
Cornell, Gary; Rosen, Michael
4
1988
The class group of an absolutely abelian \(\ell\)-extension. Zbl 0654.12006
Cornell, Gary; Rosen, Michael
4
1988
The Hilbert class field in function fields. Zbl 0632.12017
Rosen, Michael
47
1987
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.) Zbl 0662.10001
Ireland, Kenneth F.; Rosen, Michael I.
3
1987
Abelian varieties over \({\mathbb{C}}.\) (Notes by F. O. McGuinness). Zbl 0604.14032
Rosen, Michael
1
1986
The \(\ell\)-rank of the real class group of cyclotomic fields. Zbl 0551.12006
Cornell, Gary; Rosen, Michael I.
5
1984
Some remarks on the p-rank of an algebraic curve. Zbl 0524.14025
Rosen, Michael
8
1983
A classical introduction to modern number theory. (Rev. and expand. version of 1972). Zbl 0482.10001
Ireland, Kenneth; Rosen, Michael
246
1982
Units and class groups in cyclotomic function fields. Zbl 0483.12003
Galovich, Steven; Rosen, Michael
28
1982
The class number of cyclotomic function fields. Zbl 0473.12014
Galovich, Steven; Rosen, Michael
26
1981
Group-theoretic constraints on the structure of the class group. Zbl 0456.12005
Cornell, Gary; Rosen, Michael
13
1981
Abel’s theorem on the lemniscate. Zbl 0491.14023
Rosen, Michael
10
1981
Distributions on rational function fields. Zbl 0472.12013
Galovich, Steven; Rosen, Michael
6
1981
An elementary proof of the local Kronecker-Weber theorem. Zbl 0474.12014
Rosen, Michael
3
1981
Eisenstein reciprocity and \(n\)th-power residues. Zbl 0458.10002
Kraft, James; Rosen, Michael
1
1981
Cohomological analysis of the class group extension problem. Zbl 0471.12012
Cornell, Gary; Rosen, M.
1
1980
The norm map for ordinary Abelian varieties. Zbl 0417.14035
Lubin, Jonathan; Rosen, Michael I.
16
1978
Ambiguous divisor classes in function fields. Zbl 0371.12013
Rosen, Michael
17
1977
Elliptic curves and Dedekind domains. Zbl 0337.13014
Rosen, Michael
1
1976
\(S\)-units and \(S\)-class group in algebraic function fields. Zbl 0265.12003
Rosen, Michael
27
1973
The asymptotic behavior of the class group of a function field over a finite field. Zbl 0264.12003
Rosen, Michael
7
1973
Elements of number theory including an introduction to equations over finite fields. Zbl 0248.10002
Ireland, Kenneth; Rosen, Michael I.
21
1972
On the size of the Brauer group. Zbl 0182.07602
Brumer, A.; Rosen, M.
5
1968
Two theorems on Galois cohomology. Zbl 0147.04001
Rosen, Michael
7
1966
The Jacobson radical of a group algebra. Zbl 0151.02205
Rosen, M. I.
4
1966
Direct products of cyclic groups. Zbl 0136.28501
Rosen, M.
3
1966
Class number and ramification in number fields. Zbl 0128.26204
Brumer, Armand; Rosen, Michael
11
1963
all top 5

Cited by 1,948 Authors

31 Sun, Zhi-Wei
20 Jung, Hwanyup
18 Andrade, Julio Cesar
17 Bae, Sunghan
16 Lee, Yoonjin
15 Edemskiĭ, Vladimir Anatol’evich
14 Sun, Zhihong
12 Rosen, Michael I.
12 Zhang, Wenpeng
10 Gao, Peng
10 Miller, Steven J.
10 Yue, Qin
10 Zhao, Liangyi
9 Anglès, Bruno
9 Barman, Rupam
9 Hong, Shaofang
9 Lalín, Matilde Noemí
9 Schmidt, Bernhard
8 Du, Xiaoni
8 Gekeler, Ernst-Ulrich
8 Leung, Ka Hin
8 Pollack, Paul
8 Shiomi, Daisuke
8 Villa-Salvador, Gabriel Daniel
8 Wu, Hai-Liang
7 Akbary, Amir
7 Cao, Xiwang
7 Feng, Keqin
7 Florea, Alexandra M.
7 Gorodetsky, Ofir
7 Jones, Lenny K.
7 Kim, Seoyoung
7 Mesnager, Sihem
7 Oukhaba, Hassan
7 Reyes-Carocca, Sebastián
7
7 Yin, Linsheng
6 Aouissi, Siham
6 Azizi, Abdelmalek
6 David, Chantal
6 Garcia, Stephan Ramon
6 Hamahata, Yoshinori
6 Helou, Charles
6 Hu, Su
6 Ismaili, Moulay Chrif
6 Kalita, Gautam
6 Kuo, Wentang
6 Li, Chengju
6 Longhi, Ignazio
6 Nguyen Ngoc Dong Quan
6 Pan, Hao
6 Pries, Rachel J.
6 Proskurin, Nikolaĭ Vital’evich
6 Sawin, William F.
6 Sha, Min
6 Silverman, Joseph Hillel
6 Thakur, Dinesh S.
6 Zhu, Ling
5 Ahn, Jaehyun
5 Bach, Eric
5 Baier, Stephan
5 Bamunoba, Alex Samuel
5 Bary-Soroker, Lior
5 Berrizbeitia, Pedro
5 Cao, Wei
5 Coffey, Mark William
5 Cojocaru, Alina Carmen
5 Entin, Alexei
5 Feng, Tao
5 Glass, Darren B.
5 Hidalgo, Rubén Antonio
5 Hindes, Wade
5 Kawakita, Motoko Qiu
5 Keating, Jonathan Peter
5 Khosravi, Behrooz
5 Korzhik, Vladimir P.
5 Langer, Joel C.
5 Lee, Ethan Simpson
5 Lemmermeyer, Franz Josef
5 Li, Yan
5 Madan, Manohar L.
5 Momen, Zahra
5 Moree, Pieter
5 Murty, Maruti Ram
5 Pellarin, Federico
5 Saikia, Neelam
5 Scheidler, Renate
5 Wei, Fu-Tsun
5 Yang, Jing
5 Zhao, Junyong
5 Zhou, Sanming
4 Adam, David
4 Aubry, Yves
4 Bandini, Andrea
4 Bars Cortina, Francesc
4 Bayad, Abdelmejid
4 Benjamin, Elliot
4 Chen, Haimiao
4 Chipchakov, Ivan D.
4 Deng, Yingpu
...and 1,848 more Authors
all top 5

Cited in 304 Serials

260 Journal of Number Theory
105 Finite Fields and their Applications
60 Proceedings of the American Mathematical Society
55 International Journal of Number Theory
45 Transactions of the American Mathematical Society
37 Journal of Algebra
33 Designs, Codes and Cryptography
32 Mathematics of Computation
29 Journal de Théorie des Nombres de Bordeaux
26 The Ramanujan Journal
25 Archiv der Mathematik
24 Mathematische Zeitschrift
22 Acta Arithmetica
22 Journal of Combinatorial Theory. Series A
21 Discrete Mathematics
21 Manuscripta Mathematica
20 Inventiones Mathematicae
19 Rocky Mountain Journal of Mathematics
17 Bulletin of the Australian Mathematical Society
17 Journal of Pure and Applied Algebra
17 Proceedings of the Japan Academy. Series A
16 Mathematische Annalen
14 Linear Algebra and its Applications
12 Mathematical Proceedings of the Cambridge Philosophical Society
12 Integers
12 Cryptography and Communications
11 Compositio Mathematica
11 Duke Mathematical Journal
11 Functiones et Approximatio. Commentarii Mathematici
11 Acta Mathematica Sinica. English Series
11 Research in Number Theory
10 Communications in Algebra
10 Journal of Mathematical Analysis and Applications
10 Czechoslovak Mathematical Journal
10 Mathematika
9 American Mathematical Monthly
9 Monatshefte für Mathematik
9 Advances in Mathematics of Communications
8 Theoretical Computer Science
8 Forum Mathematicum
8 Applicable Algebra in Engineering, Communication and Computing
8 Journal of Mathematical Sciences (New York)
8 Journal of Mathematics
7 Communications in Mathematical Physics
7 Israel Journal of Mathematics
7 Journal of Symbolic Computation
7 Journal of Combinatorial Designs
7 Journal of Integer Sequences
7 Journal of the Australian Mathematical Society
7 Science China. Mathematics
7 AIMS Mathematics
6 Acta Mathematica Hungarica
6 Expositiones Mathematicae
6 Experimental Mathematics
6 Turkish Journal of Mathematics
6 Comptes Rendus. Mathématique. Académie des Sciences, Paris
6 Journal of Applied Mathematics and Computing
6 Research in the Mathematical Sciences
6 European Journal of Mathematics
5 Discrete Applied Mathematics
5 Information Processing Letters
5 Mathematical Notes
5 The Mathematical Intelligencer
5 Advances in Mathematics
5 Colloquium Mathematicum
5 Journal für die Reine und Angewandte Mathematik
5 Nagoya Mathematical Journal
5 Proceedings of the London Mathematical Society. Third Series
5 Tokyo Journal of Mathematics
5 European Journal of Combinatorics
5 Elemente der Mathematik
5 Bulletin of the American Mathematical Society. New Series
5 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
5 Taiwanese Journal of Mathematics
5 Journal of Algebra and its Applications
5 Algebra & Number Theory
5 Korean Journal of Mathematics
5 Electronic Research Archive
4 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
4 Bulletin of the London Mathematical Society
4 Canadian Journal of Mathematics
4 Journal of Combinatorial Theory. Series B
4 Graphs and Combinatorics
4 Journal of the American Mathematical Society
4 Journal of Cryptology
4 Geometric and Functional Analysis. GAFA
4 Journal of Algebraic Combinatorics
4 Advances in Geometry
4 JP Journal of Algebra, Number Theory and Applications
4 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
3 Periodica Mathematica Hungarica
3 Bulletin de la Société Mathématique de France
3 Glasgow Mathematical Journal
3 Illinois Journal of Mathematics
3 Journal of Computational and Applied Mathematics
3 Journal of the Korean Mathematical Society
3 Journal of Soviet Mathematics
3 Pacific Journal of Mathematics
3 Siberian Mathematical Journal
3 Topology and its Applications
...and 204 more Serials
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Cited in 51 Fields

1,395 Number theory (11-XX)
305 Algebraic geometry (14-XX)
195 Combinatorics (05-XX)
140 Information and communication theory, circuits (94-XX)
89 Group theory and generalizations (20-XX)
75 Field theory and polynomials (12-XX)
63 Special functions (33-XX)
43 Commutative algebra (13-XX)
38 Computer science (68-XX)
32 Dynamical systems and ergodic theory (37-XX)
30 Manifolds and cell complexes (57-XX)
24 Associative rings and algebras (16-XX)
23 Linear and multilinear algebra; matrix theory (15-XX)
20 Quantum theory (81-XX)
19 Geometry (51-XX)
13 Real functions (26-XX)
13 Functions of a complex variable (30-XX)
13 Harmonic analysis on Euclidean spaces (42-XX)
12 History and biography (01-XX)
12 Topological groups, Lie groups (22-XX)
11 Mathematical logic and foundations (03-XX)
11 Numerical analysis (65-XX)
10 Order, lattices, ordered algebraic structures (06-XX)
10 \(K\)-theory (19-XX)
9 Nonassociative rings and algebras (17-XX)
9 Probability theory and stochastic processes (60-XX)
8 Measure and integration (28-XX)
8 Algebraic topology (55-XX)
6 Approximations and expansions (41-XX)
6 Convex and discrete geometry (52-XX)
6 Operations research, mathematical programming (90-XX)
4 Partial differential equations (35-XX)
3 General and overarching topics; collections (00-XX)
3 Several complex variables and analytic spaces (32-XX)
3 Abstract harmonic analysis (43-XX)
3 Differential geometry (53-XX)
3 General topology (54-XX)
3 Statistical mechanics, structure of matter (82-XX)
3 Mathematics education (97-XX)
2 Category theory; homological algebra (18-XX)
2 Sequences, series, summability (40-XX)
2 Global analysis, analysis on manifolds (58-XX)
2 Statistics (62-XX)
2 Relativity and gravitational theory (83-XX)
1 Ordinary differential equations (34-XX)
1 Difference and functional equations (39-XX)
1 Functional analysis (46-XX)
1 Mechanics of deformable solids (74-XX)
1 Optics, electromagnetic theory (78-XX)
1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
1 Biology and other natural sciences (92-XX)

Citations by Year

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