## Found 365 Documents (Results 1–100)

100
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### Existence of the continued fractions of $$\sqrt{d}$$ and its applications. (English)Zbl 07556741

MSC:  11A55 11R11 11R27
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### On a polynomial involving roots of unity and its applications. (English)Zbl 07543097

MSC:  11R18 11R11 11R27
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### A note on power integral bases in pure quartic number fields. (English)Zbl 07479521

MSC:  11D25 11R16
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### Relative class number one problem of real quadratic fields and continued fraction of $$\sqrt{m}$$ with period 6. (English)Zbl 07546031

MSC:  11R11 11R65
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### On fundamental $$S$$-units and continued fractions constructed in hyperelliptic fields using two linear valuations. (English. Russian original)Zbl 1475.11133

Dokl. Math. 103, No. 3, 151-156 (2021); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 498, 65-70 (2021).
MSC:  11J70 11R58 11R27
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### Fundamental units for real quadratic fields determined by continued fraction conditions. (English)Zbl 1484.11208

MSC:  11R27 11A55 11R11
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### Periodic elements $$\sqrt{f}$$ in elliptic fields with a field of constants of zero characteristic. (Russian. English summary)Zbl 1455.11155

MSC:  11R58 11J70 11R27
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### Diophantine equation generated by the maximal subfield of a circular field. (English. Russian original)Zbl 1456.11203

Russ. Math. 64, No. 7, 38-47 (2020); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2020, No. 7, 45-55 (2020).
MSC:  11R04 11R16 11D25
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### Divisibility of class number of a real cubic or quadratic field and its fundamental unit. (English)Zbl 1444.11221

Chakraborty, Kalyan (ed.) et al., Class groups of number fields and related topics. Collected papers presented at the first international conference, ICCGNFRT, Harish-Chandra Research Institute, Allahabad, India, September 4–7, 2017. Singapore: Springer. 67-72 (2020).
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### On $$S$$-units for valuations of the second degree in hyperelliptic fields. (English. Russian original)Zbl 1457.11159

Izv. Math. 84, No. 2, 392-435 (2020); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 84, No. 2, 197-242 (2020).
MSC:  11R58 11J70 11R27
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### A family of pairs of imaginary cyclic fields of degree $$(p-1)/2$$ with both class numbers divisible by $$p$$. (English)Zbl 1447.11113

MSC:  11R11 11R16 11R29
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### The criterion of periodicity of continued fractions of key elements in hyperelliptic fields. (Russian. English summary)Zbl 1439.11286

MSC:  11R58 11G16 11J70
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### Periodic Jacobi-Perron algorithms in cubic fields and fundamental units. (English)Zbl 1431.11121

MSC:  11R16 11R27 11A55
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### A family of cyclic quartic fields with explicit fundamental units. (English)Zbl 1442.11141

MSC:  11R16 11R27
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### Periodic continued fractions and $$S$$-units with second degree valuations in hyperelliptic fields. (Russian. English summary)Zbl 1434.11130

MSC:  11J70 11G16
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### Fundamental units and consecutive squarefull numbers. (English)Zbl 1419.11006

MSC:  11A25 11D09
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### From Diophantine approximations to Diophantine equations. (Russian. English summary)Zbl 1435.11089

MSC:  11H55 11J70
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### A note on the negative Pell equation. (English)Zbl 1407.11127

Sander, Jürgen (ed.) et al., From arithmetic to zeta-functions. Number theory in memory of Wolfgang Schwarz. Cham: Springer. 31-40 (2016).
MSC:  11R29 11R27 11D09
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### Fundamental units for orders of unit rank 1 and generated by a unit. (English)Zbl 1411.11107

Gładki, Paweł (ed.) et al., Algebra, logic and number theory. Proceedings of the 3rd joint conferences on algebra, logic and number theory, Bȩdlewo, Poland, June 8–13, 2014. Warsaw: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-31-7/pbk). Banach Center Publications 108, 173-189 (2016).
MSC:  11R27 11R54 11R16
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### Families of cyclic cubic fields. (English)Zbl 1414.11132

MSC:  11R16 11R27
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### Group ring groups. Volume 2: Structure theorems of unit groups. (English)Zbl 1338.16002

De Gruyter Textbook. Berlin: De Gruyter (ISBN 978-3-11-041149-2/pbk; 978-3-11-041150-8/ebook). x, 217 p. (2016).
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### An algorithm for explicit form of fundamental units of certain real quadratic fields and period eight. (English)Zbl 1389.11015

MSC:  11A55 11R27
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### Ramification in relative quadratic extensions and fundamental units of real quadratic fields. (English)Zbl 1349.11135

MSC:  11R11 11R27
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### On the Dedekind zeta function. II. (English. Russian original)Zbl 1360.11123

J. Math. Sci., New York 207, No. 6, 923-933 (2015); translation from Zap. Nauchn. Semin. POMI 429, 178-192 (2014).
MSC:  11R42 11R44
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### On systems of fundamental units of certain quartic fields. (English)Zbl 1331.11099

MSC:  11R27 11R16 11R29
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### Determination of the orders generated by a cyclic cubic unit that are Galois invariant. (English)Zbl 1394.11073

MSC:  11R16 11R27
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### Explicit form of fundamental units of certain real quadratic fields. (English)Zbl 1389.11014

MSC:  11A55 11R11 11R27
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### A note on modular curves and fundamental units of negative norm. (English)Zbl 1367.11078

MSC:  11R27 11F41
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### On units of a family of cubic number fields. (English)Zbl 1358.11123

MSC:  11R27 11R16 11R37

### A method for finding a minimal point of the lattice in cubic number fields. II. (English)Zbl 1311.11101

MSC:  11R16 11R27
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### On the fundamental units of some cubic orders generated by units. (English)Zbl 1307.11120

MSC:  11R27 11R16
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### Signed Shintani cones for number fields with one complex place. (English)Zbl 1307.11119

MSC:  11R27 11R42 11Y40
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### A method for finding a minimal point of the lattice in cubic number fields. (English)Zbl 1305.11092

MSC:  11R16 11R27
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### Number-theoretic properties of hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves over the rational number field. (English. Russian original)Zbl 1305.11096

Russ. Math. Surv. 69, No. 1, 1-34 (2014); translation from Usp. Mat. Nauk 69, No. 1, 3-38 (2014).
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### Fundamental units of real quadratic fields of odd class number. (English)Zbl 1310.11110

MSC:  11R27 11D09
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### On arithmetic monodromy representations of Eisenstein type in fundamental groups of once punctured elliptic curves. (English)Zbl 1330.14048

MSC:  14H30 11G16 11F20
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### Algebraic theory of quadratic numbers. (English)Zbl 1280.11002

Universitext. New York, NY: Springer (ISBN 978-1-4614-7716-7/pbk; 978-1-4614-7717-4/ebook). xi, 197 p. (2013).
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### On the torsion problem in Jacobians of curves of genus 2 over the rational number field. (English. Russian original)Zbl 1345.11045

Dokl. Math. 86, No. 2, 642-643 (2012); translation from Dokl. Akad. Nauk. 446, No. 3, 263-264 (2012).
MSC:  11G30 14H40 14H25
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### On the class number and the fundamental unit of the real quadratic field $$k = \mathbb Q (\sqrt {pq})$$. (English)Zbl 1294.11189

MSC:  11R11 11R27 11R29
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### Colmez cones for fundamental units of totally real cubic fields. (English)Zbl 1257.11097

MSC:  11R16 11R27
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### On the fundamental units of a totally real cubic order generated by a unit. (English)Zbl 1283.11152

MSC:  11R16 11R27
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### Searching discriminants with large fundamental units via continued fraction expansion. (English)Zbl 1307.11012

Amou, Masaaki (ed.) et al., Diophantine analysis and related fields 2011, DARF–2011. Proceedings of the conference, Musashino, Tokyo, Japan, March 3–5, 2011. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0947-7/pbk). AIP Conference Proceedings 1385, 38-41 (2011).
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### On continued fractions of real quadratic fields with period six. (English)Zbl 1248.11086

MSC:  11R27 11R11 11A55
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### Deconstruction of a Dirichlet-Nazimow formula. (English)Zbl 1287.11126

MSC:  11R29 11R37 11R42
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### Fundamentality of a cubic unit $$u$$ for $$\mathbb{Z}[u]$$. (English)Zbl 1231.11128

MSC:  11R27 11R16
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### A new local-global principle for quadratic function fields. (English. Russian original)Zbl 1244.11093

Dokl. Math. 82, No. 1, 531-534 (2010); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 433, No. 2, 154-157 (2010).
MSC:  11R58 11R27
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### Optimal systems of fundamental $$S$$-units for LLL-reduction. (English)Zbl 1199.11135

MSC:  11R27 11D61 11Y50
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### Some results on the class numbers of certain real quadratic fields. (English)Zbl 1198.11084

MSC:  11R11 11R29 11R27
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### The class number one problem for some totally complex quartic number fields. (English)Zbl 1167.11040

MSC:  11R29 11R27 11R16
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### A note on characterization of $$\mathcal N_{\mathcal U}(D_n)$$. (English)Zbl 1163.16303

MSC:  16U60 20C05 16S34

### Computing fundamental units in bicyclic biquadratic global fields. (English)Zbl 1173.11057

MSC:  11R16 11R27

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### Upper bounds of the class number and the fundamental unit of real quadratic field $$\mathbb{Q}(\sqrt p)$$. (Chinese. English summary)Zbl 1131.11350

MSC:  11R11 11R27 11R29

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### Units in some parametric families of quartic fields. (English)Zbl 1116.11090

MSC:  11R27 11R16
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### Fundamental units in a parametric family of not totally real quintic number fields. (English)Zbl 1119.11065

MSC:  11R27 11R21
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### On congruence relations between the fundamental units of biquadratic fields. (English)Zbl 1171.11327

MSC:  11R16 11R27 11R42
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### Congruences between cusp forms and fundamental units. (Japanese. English summary)Zbl 1390.11085

MSC:  11F33 11R27 11B68
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### On the units of certain number fields of degree 8 over $$\mathbb Q$$. (Sur les unités de certains corps de nombres de degré 8 sur $$\mathbb Q$$.) (French)Zbl 1188.11056

MSC:  11R27 11R21
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### Fundamental units in a family of cubic fields. (English)Zbl 1079.11056

MSC:  11R27 11R16 11Y40
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### Separable free quadratic algebras over quadratic integers. (English)Zbl 1072.11079

MSC:  11R11 11R27 11S15
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### On Tate-Shafarevich groups of $$y^2=x(x^2-k^2)$$. (English)Zbl 1097.11012

MSC:  11D09 11A55 11R11
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