# zbMATH — the first resource for mathematics

## Thaine, Francisco

 Author ID: thaine.francisco Published as: Thaine, F.; Thaine, Francisco
 Documents Indexed: 15 Publications since 1982

#### Co-Authors

 15 single-authored
all top 5

#### Serials

 3 Journal of Number Theory 2 Mathematics of Computation 2 Michigan Mathematical Journal 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Journal of Pure and Applied Algebra 1 Manuscripta Mathematica 1 Proceedings of the American Mathematical Society 1 Transactions of the American Mathematical Society 1 Experimental Mathematics 1 Annals of Mathematics. Second Series 1 Journal of Combinatorics and Number Theory

#### Fields

 15 Number theory (11-XX) 1 Combinatorics (05-XX) 1 Field theory and polynomials (12-XX)

#### Citations contained in zbMATH Open

13 Publications have been cited 74 times in 51 Documents Cited by Year
On the ideal class groups of real abelian number fields. Zbl 0665.12003
Thaine, Francisco
1988
Properties that characterize Gaussian periods and cyclotomic numbers. Zbl 0862.11059
Thaine, F.
1996
Families of irreducible polynomials of Gaussian periods and matrices of cyclotomic numbers. Zbl 0989.11055
Thaine, F.
2000
On the coefficients of Jacobi sums in prime cyclotomic fields. Zbl 0944.11036
Thaine, F.
1999
Jacobi sums and new families of irreducible polynomials of Gaussian periods. Zbl 0989.11056
Thaine, F.
2001
On the $$p$$-part of the ideal class group of $$\mathbb{Q} (\zeta_ p + \zeta_ p^{-1})$$ and Vandiver’s conjecture. Zbl 0844.11069
Thaine, F.
1995
Polynomials generalizing binomial coefficients and their application to the study of Fermat’s last theorem. Zbl 0504.10009
Thaine, F.
1982
On Gaussian periods that are rational integers. Zbl 1027.11081
Thaine, F.
2002
On the orders of ideal classes in prime cyclotomic fields. Zbl 0717.11046
Thaine, Francisco
1990
Cyclic polynomials and the multiplication matrices of their roots. Zbl 1041.11069
Thaine, F.
2004
On the first case of Fermat’s last theorem. Zbl 0571.10016
Thaine, Francisco
1985
On the relation between units and Jacobi sums in prime cyclotomic fields. Zbl 0760.11030
Thaine, Francisco
1991
On Fermat’s last theorem and the arithmetic of $${\mathbb{Z}}[\zeta _ p+\zeta _ p^{-1}]$$. Zbl 0654.10018
Thaine, Francisco
1988
Cyclic polynomials and the multiplication matrices of their roots. Zbl 1041.11069
Thaine, F.
2004
On Gaussian periods that are rational integers. Zbl 1027.11081
Thaine, F.
2002
Jacobi sums and new families of irreducible polynomials of Gaussian periods. Zbl 0989.11056
Thaine, F.
2001
Families of irreducible polynomials of Gaussian periods and matrices of cyclotomic numbers. Zbl 0989.11055
Thaine, F.
2000
On the coefficients of Jacobi sums in prime cyclotomic fields. Zbl 0944.11036
Thaine, F.
1999
Properties that characterize Gaussian periods and cyclotomic numbers. Zbl 0862.11059
Thaine, F.
1996
On the $$p$$-part of the ideal class group of $$\mathbb{Q} (\zeta_ p + \zeta_ p^{-1})$$ and Vandiver’s conjecture. Zbl 0844.11069
Thaine, F.
1995
On the relation between units and Jacobi sums in prime cyclotomic fields. Zbl 0760.11030
Thaine, Francisco
1991
On the orders of ideal classes in prime cyclotomic fields. Zbl 0717.11046
Thaine, Francisco
1990
On the ideal class groups of real abelian number fields. Zbl 0665.12003
Thaine, Francisco
1988
On Fermat’s last theorem and the arithmetic of $${\mathbb{Z}}[\zeta _ p+\zeta _ p^{-1}]$$. Zbl 0654.10018
Thaine, Francisco
1988
On the first case of Fermat’s last theorem. Zbl 0571.10016
Thaine, Francisco
1985
Polynomials generalizing binomial coefficients and their application to the study of Fermat’s last theorem. Zbl 0504.10009
Thaine, F.
1982
all top 5

#### Cited by 41 Authors

 8 Thaine, Francisco 5 Rubin, Karl Cooper 3 All, Timothy 3 Hoshi, Akinari 3 Kučera, Radan 3 Seo, Soogil 2 Bhandari, Ashwani K. 2 Grover, Pooja 2 Hashimoto, Ki-ichiro 2 Mihăilescu, Preda 1 Aoki, Miho 1 Baccar, N. 1 Bennett, Michael A. 1 Buckingham, Paul Richard 1 Cassou-Noguès, Philippe 1 Chapdelaine, Hugo 1 Darmon, Henri René 1 Gras, Georges 1 Greither, Cornelius 1 Harder, Günter 1 Ichimura, Humio 1 Kurihara, Fumika 1 Lettl, Günter Hermann Alexander 1 Louboutin, Stéphane R. 1 Mazur, Barry 1 Metsänkylä, Tauno 1 Pink, Richard 1 Qin, Hourong 1 Schoof, René 1 Sharma, Amit K. 1 Sharma, Anuradha 1 Shen, Qiqing 1 Siksek, Samir 1 Silverberg, Alice 1 Solomon, David R. 1 Tateyama, Koichi 1 Taylor, Martin J. 1 van Wamelen, Paul B. 1 Wan, Xin 1 Washington, Lawrence C. 1 Wu, Fan
all top 5

#### Cited in 23 Serials

 11 Journal of Number Theory 6 Inventiones Mathematicae 5 Mathematics of Computation 4 Proceedings of the Japan Academy. Series A 3 Bulletin of the American Mathematical Society. New Series 2 Journal für die Reine und Angewandte Mathematik 2 Proceedings of the American Mathematical Society 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Annales de l’Institut Fourier 1 Canadian Journal of Mathematics 1 Journal of Pure and Applied Algebra 1 Mathematische Nachrichten 1 Nagoya Mathematical Journal 1 Tohoku Mathematical Journal. Second Series 1 Tokyo Journal of Mathematics 1 Transactions of the American Mathematical Society 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Finite Fields and their Applications 1 Journal of Combinatorial Designs 1 Journal of the Australian Mathematical Society 1 Asian-European Journal of Mathematics 1 Discrete Mathematics, Algorithms and Applications 1 Science China. Mathematics
all top 5

#### Cited in 6 Fields

 45 Number theory (11-XX) 8 Algebraic geometry (14-XX) 4 Field theory and polynomials (12-XX) 3 Information and communication theory, circuits (94-XX) 2 Group theory and generalizations (20-XX) 1 Combinatorics (05-XX)