Found 568 Documents (Results 1–100)
Higher reciprocity law and an analogue of the Grunwald-Wang theorem for the ring of polynomials over an ultra-finite field. (English) Zbl 07827508
Hermite’s identity and the quadratic reciprocity law. (English) Zbl 1543.11003
Reviewer: Rusen Li (Xiangtan)
Elementary algebra and number theory. 3rd edition. (Elementare Algebra und Zahlentheorie.) (German) Zbl 1531.11003
Mathematik Kompakt. Cham: Birkhäuser (ISBN 978-3-031-39770-7/pbk; 978-3-031-39771-4/ebook). xiii, 199 p. (2023).
An amazing identity of Gauss and Jenkins’ lemma. (English) Zbl 1533.11147
Reviewer: Alexey Ustinov (Khabarovsk)
Legendre-Teege quadratic reciprocity. (English) Zbl 1522.11001
Reviewer: Albert C. Lewis (Austin)
Darmon points on elliptic curves over totally real fields. (English) Zbl 1526.11027
Reviewer: Matteo Longo (Padova)
Gaussian sums and their application to the proof of quadratic reciprocity law. (Russian. English summary) Zbl 1504.11005
Some arithmetical properties of linear recurring sequences in a finite field. (English) Zbl 1513.11030
Extended Galbraith’s test on the anonymity of IBE schemes from higher residuosity. (English) Zbl 1481.94129
On local symbols and the reciprocity law for foliated dynamical systems on 3-manifolds: research announcement. (English) Zbl 1461.11069
Reciprocity by resultant in \(k[t]\). (English) Zbl 1471.11012
Reviewer: Franz Lemmermeyer (Jagstzell)
Number theory revealed: a masterclass. (English) Zbl 1454.11002
Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-4158-6/hbk; 978-1-4704-5424-1/ebook). xxviii, 587 p. (2019).
Reviewer: Franz Lemmermeyer (Jagstzell)
Number theory revealed: an introduction. (English) Zbl 1454.11001
Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-4157-9/hbk; 978-1-4704-5423-4/ebook). xxiv, 264 p. (2019).
Reviewer: Franz Lemmermeyer (Jagstzell)
A minimalist proof of the law of quadratic reciprocity. (English) Zbl 1427.11006
Reviewer: Franz Lemmermeyer (Jagstzell)
MSC:
11A15
Primality testing for numbers of the form \(h\cdot 2^n\pm 1\). (English) Zbl 1423.11207
Reviewer: Dimitros Poulakis (Thessaloniki)
Elementary algebra and number theory. 2nd corrected and updated edition. (Elementare Algebra und Zahlentheorie.) (German) Zbl 1429.11003
Mathematik Kompakt. Cham: Birkhäuser (ISBN 978-3-030-25297-7/pbk; 978-3-030-25298-4/ebook). xi, 170 p. (2019).
Construction of class fields over imaginary biquadratic fields. (English) Zbl 1437.11084
Reviewer: Abdelmalek Azizi (Oujda)
Combinatorial duality for Poincaré series, polytopes and invariants of plumbed 3-manifolds. (English) Zbl 1475.32015
Reviewer: Dmitry Kerner (Rehovot)
Small prime \(k\)th power residues for \(k=2,3,4\): a reciprocity laws approach. (English) Zbl 1454.11008
Reviewer: Franz Lemmermeyer (Jagstzell)
On arithmetic of the superspecial locus. (English) Zbl 1408.14137
Reviewer: Herbert Lange (Erlangen)
Yet another proof of the quadratic reciprocity law. (English) Zbl 1441.11006
Reviewer: Franz Lemmermeyer (Jagstzell)
An explicit reciprocity law associated to some finite coverings of algebraic curves. (English) Zbl 1420.19006
Reviewer: Piotr Krasoń (Szczecin)
David Hilbert: The theory of algebraic number fields. Jahresber. Deutsche Math. Ver. 4 (1897), 175–546. (David Hilbert: Die Theorie der algebraischen Zahlkörper. Jahresber. Deutsche Math. Ver. 4 (1897), 175–546.) (English) Zbl 1397.01016
Reviewer: Stefan Neuwirth (Besançon)
Explicit constructions and the arithmetic of local number fields. (English. Russian original) Zbl 1433.11130
Vestn. St. Petersbg. Univ., Math. 50, No. 3, 242-264 (2017); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 4(62), No. 3, 402-435 (2017).
Gauss’ lemma over function fields. (English) Zbl 1445.11134
Reviewer: Franz Lemmermeyer (Jagstzell)
Polynomial power residue symbols and \(q\)-resultants. (English. French summary) Zbl 1429.11219
A rational reciprocity law over function fields. (English) Zbl 1427.11003
Reviewer: Franz Lemmermeyer (Jagstzell)
Reciprocity laws and \(K\)-theory. (English) Zbl 1354.19003
Reviewer: Thong Nguyen Quang Do (Besançon)
MSC:
19F15
Coates-Wiles homomorphisms and Iwasawa cohomology for Lubin-Tate extensions. (English) Zbl 1409.11107
Loeffler, David (ed.) et al., Elliptic curves, modular forms and Iwasawa theory. In honour of John H. Coates’ 70th birthday, Cambridge, UK, March 2015. Proceedings of the conference and the workshop. Cham: Springer. Springer Proc. Math. Stat. 188, 401-468 (2016).
New trigonometric identities and reciprocity laws of generalized Dedekind sums. (English) Zbl 1416.11062
Reviewer: Kaori Ota (Tokyo)
Rational structure of \(X(N)\) over \(\mathbb{Q}\) and explicit Galois action on CM points. (English) Zbl 1422.11141
Asymmetric ID-based encryption system, using an explicit pairing function of the reciprocity law. (English) Zbl 1360.94336
Quadratic residues and non-residues. Selected topics. (English) Zbl 1353.11001
Lecture Notes in Mathematics 2171. Cham: Springer (ISBN 978-3-319-45954-7/pbk; 978-3-319-45955-4/ebook). xiii, 292 p. (2016).
Reviewer: Enzo Bonacci (Latina)
The two-dimensional Contou-Carrère symbol and reciprocity laws. (English) Zbl 1346.19003
Reviewer: Kevin Hutchinson (Dublin)
MSC:
19D45
Galois action on special theta values. (English. French summary) Zbl 1417.11042
Higher reciprocity laws and rational points. (Lois de réciprocité supérieures et points rationnels.) (French. English summary) Zbl 1360.11068
Reviewer: Yong Hu (Caen Cedex)
Integral Tate modules and splitting of primes in torsion fields of elliptic curves. (English) Zbl 1408.11055
Reciprocity laws and Galois representations: recent breakthroughs. (English) Zbl 1330.11071
Reviewer: Abdelmalek Azizi (Oujda)
Explicit reciprocity law of Bloch-Kato and exponential maps. (English) Zbl 1398.11102
Coates, John (ed.) et al., The Bloch-Kato conjecture for the Riemann zeta function. Proceedings of the workshop ’The Bloch-Kato conjecture for the Riemann zeta function at the odd positive integers’, Pune, India, July 1012. Cambridge: Cambridge University Press (ISBN 978-1-107-49296-7/pbk). 65-96 (2015).
The arithmetic of the Lubin-Tate formal module in a multidimensional complete field. (English) Zbl 1334.11088
St. Petersbg. Math. J. 26, No. 6, 859-865 (2015); translation from Algebra Anal. 26, No. 6, 1-9 (2014).
Some new evaluations of the Legendre symbol \(\bigl(\frac{a+b\sqrt{q}}{p}\bigr)\). (English) Zbl 1384.11004
Reviewer: Franz Lemmermeyer (Jagstzell)
Primality test for numbers of the form \(A p^n + w_n\). (English) Zbl 1364.11160
Reviewer: Franz Lemmermeyer (Jagstzell)
Primality test for numbers of the form \((2p)^{2^n}+1\). (English) Zbl 1370.11139
Reviewer: Othman Echi (Dhahran)
Congruences for \(q^{[p/8]}\pmod p\) under the condition \(4n^2p = x^2 + qy^2\). (English) Zbl 1390.11012
Primitive generators of certain class fields. (English) Zbl 1319.11081
Reviewer: Abdelmalek Azizi (Oujda)
On Eisenstein reciprocity. (English) Zbl 1316.11005
Reviewer: Franz Lemmermeyer (Jagstzell)
The quadratic reciprocity law. A collection of classical proofs. Edited and translated from the German by Franz Lemmermeyer. (English) Zbl 1338.11003
Cham: Birkhäuser/Springer (ISBN 978-3-319-16282-9/hbk; 978-3-319-16283-6/ebook). xiv, 172 p. (2015).
Reviewer: Manouchehr Misaghian (Prairie View)
Application of Weierstrass units to relative power integral bases. (English) Zbl 1326.11063
Reviewer: Péter Olajos (Miskolc)
Generating functions of even Dedekind symbols with polynomial reciprocity laws. (English) Zbl 1368.11041
Kato’s Euler system in families. I. (Le système d’Euler de Kato en famille. I.) (French. English summary) Zbl 1311.11032
Reviewer: Laurent Berger (Lyon)
On the sum of two integral squares in the imaginary quadratic field \(\mathbb Q(\sqrt {-2p})\). (English) Zbl 1365.11038
On some theta constants and class fields. (English) Zbl 1311.11038
Reviewer: G. K. Sankaran (Bath)
Relations for Bernoulli-Barnes numbers and Barnes zeta functions. (English) Zbl 1369.11018
Reviewer: Kaori Ota (Tokyo)
Algebraic number theory. (English) Zbl 1303.11001
Springer Undergraduate Mathematics Series. Cham: Springer (ISBN 978-3-319-07544-0/pbk; 978-3-319-07545-7/ebook). xiii, 292 p. (2014).
Reviewer: Franz Lemmermeyer (Jagstzell)
The quadratic Gauss sum redux. (English) Zbl 1378.11011
Reviewer: Franz Lemmermeyer (Jagstzell)
Permutations and reciprocity law according to Zolotarev-Frobenius-Rousseau. (Russian. English summary) Zbl 1423.11018
MSC:
11A15
On the non-abelian global class field theory. (English) Zbl 1318.11145
Reviewer: Günter Lettl (Graz)
MSC:
11R39
Kato’s Euler system. (Le système d’Euler de Kato.) (French. English summary) Zbl 1311.11055
Construction of the heptadecagon and quadratic reciprocity. (English) Zbl 1362.11003
Reviewer: Franz Lemmermeyer (Jagstzell)
Gauß and Dirichlet – an episode. (Gauß und Dirichlet – eine Episode.) (German) Zbl 1288.01015
Reviewer: Karin Reich (Berlin)
The product of symbols of \(p^n\)th power residues as an abelian integral. (English. Russian original) Zbl 1336.11005
St. Petersbg. Math. J. 24, No. 2, 275-281 (2013); translation from Algebra Anal. 24, No. 2, 120-129 (2012).
Reviewer: Franz Lemmermeyer (Jagstzell)
MSC:
11A15
On the Diophantine equation \(x^2 - Dy^2 = n\). (English) Zbl 1281.11026
Reviewer: Olaf Ninnemann (Berlin)
Reciprocity laws through formal groups. (English) Zbl 1336.11004
Reviewer: Franz Lemmermeyer (Jagstzell)
Gauss’s laws of reciprocity of number theory. A complete representation of the posthumous works in modern form. (Gauß’ Reziprozitätsgesetze der Zahlentheorie. Eine Gesamtdarstellung der Hinterlassenschaft in zeitgemäßer Form.) (German) Zbl 1270.01005
Algorismus 78. Augsburg: ERV Dr. Erwin Rauner Verlag (ISBN 978-3-936905-52-6/pbk). xiii, 281 p. (2013).
Reviewer: Albert C. Lewis (Austin)
The Eisenstein reciprocity law for formal Lubin-Tate groups. (English. Russian original) Zbl 1300.11121
J. Math. Sci., New York 180, No. 3, 269-277 (2012); translation from Zap. Nauchn. Semin. POMI 386, 129-143 (2011).
MSC:
11S31
Mersenne primes in real quadratic fields. (English) Zbl 1290.11141
Reviewer: Franz Lemmermeyer (Jagstzell)
Sequences of Dedekind sums in function fields. (English) Zbl 1282.11036
Lavrauw, Michel (ed.) et al., Theory and applications of finite fields. The 10th international conference on finite fields and their applications, Ghent, Belgium, July 11–15, 2011. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-5298-9/pbk; 978-0-8218-9157-5/ebook). Contemporary Mathematics 579, 81-89 (2012).
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