Chan, Heng Huat; Chan, Song Heng An amazing identity of Gauss and Jenkins’ lemma. (English) Zbl 07734856 Bull. Aust. Math. Soc. 108, No. 1, 86-98 (2023). Reviewer: Alexey Ustinov (Khabarovsk) MSC: 11L05 11A07 11A15 PDFBibTeX XMLCite \textit{H. H. Chan} and \textit{S. H. Chan}, Bull. Aust. Math. Soc. 108, No. 1, 86--98 (2023; Zbl 07734856) Full Text: DOI
Castillo, John H.; Mainguez, Jhony Fernando Caranguay The set of \(k\)-units modulo \(n\). (English) Zbl 1512.11001 Involve 15, No. 3, 367-378 (2022). Reviewer: Antonio M. Oller Marcén (Zaragoza) MSC: 11A05 11A07 11A15 16U60 PDFBibTeX XMLCite \textit{J. H. Castillo} and \textit{J. F. C. Mainguez}, Involve 15, No. 3, 367--378 (2022; Zbl 1512.11001) Full Text: DOI arXiv
Wei, Yangjiang; Su, Huadong; Liang, Linhua Unit group structure of the quotient ring of a quadratic ring. (English) Zbl 1510.11154 J. Algebra Appl. 21, No. 12, Article ID 2350010, 31 p. (2022). Reviewer: Peter Danchev (Sofia) MSC: 11R11 16U60 11R04 11A07 PDFBibTeX XMLCite \textit{Y. Wei} et al., J. Algebra Appl. 21, No. 12, Article ID 2350010, 31 p. (2022; Zbl 1510.11154) Full Text: DOI
Varchenko, Alexander [Sperber, Steven] Notes on solutions of KZ equations modulo \(p^s\) and \(p\)-adic limit \(s\to\infty\). (English) Zbl 1497.13020 Koelink, Erik (ed.) et al., Hypergeometry, integrability and Lie theory. Virtual conference, Lorentz Center, Leiden, the Netherlands, December 7–11, 2020. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 780, 309-347 (2022). MSC: 13A35 11G25 14G10 33C60 32G20 PDFBibTeX XMLCite \textit{A. Varchenko}, Contemp. Math. 780, 309--347 (2022; Zbl 1497.13020) Full Text: DOI arXiv
Beukers, Frits; Delaygue, Eric Some supercongruences of arbitrary length. (English) Zbl 1517.11002 Indag. Math., New Ser. 33, No. 5, 946-955 (2022). MSC: 11A07 33C05 11B65 PDFBibTeX XMLCite \textit{F. Beukers} and \textit{E. Delaygue}, Indag. Math., New Ser. 33, No. 5, 946--955 (2022; Zbl 1517.11002) Full Text: DOI arXiv
Gallardo, L. H. Ryser’s conjecture under linear constraints. (English) Zbl 1497.11266 Algebra Discrete Math. 33, No. 1, 30-37 (2022). Reviewer: Roksana Słowik (Gliwice) MSC: 11R18 15B34 11A07 PDFBibTeX XMLCite \textit{L. H. Gallardo}, Algebra Discrete Math. 33, No. 1, 30--37 (2022; Zbl 1497.11266) Full Text: Link
Gallardo, Luis Abelian subgroup of \(O_4(Q)\) related to Ryser’s conjecture. (English) Zbl 1490.15047 Gulf J. Math. 12, No. 1, 56-61 (2022). Reviewer: Francesco Battistoni (Milano) MSC: 15B34 15B05 11R18 20K27 20K01 PDFBibTeX XMLCite \textit{L. Gallardo}, Gulf J. Math. 12, No. 1, 56--61 (2022; Zbl 1490.15047) Full Text: Link
Ward, Jacob The \(q\)-unit circle: the unit circle in prime characteristics and its properties. (English) Zbl 1436.11140 Finite Fields Appl. 58, 222-256 (2019). Reviewer: Gabriel D. Villa Salvador (Ciudad de México) MSC: 11R60 11R32 11R58 11T22 11T55 12E20 52C26 PDFBibTeX XMLCite \textit{J. Ward}, Finite Fields Appl. 58, 222--256 (2019; Zbl 1436.11140) Full Text: DOI
Sander, J. W. Multiplicative atom decomposition of sets of exceptional units in residue class rings. (English) Zbl 1420.11010 J. Number Theory 173, 254-271 (2017). MSC: 11A07 11T30 06E20 PDFBibTeX XMLCite \textit{J. W. Sander}, J. Number Theory 173, 254--271 (2017; Zbl 1420.11010) Full Text: DOI
Smpokos, Konstantinos An algebraic treatment of congruences in number theory. (English) Zbl 1425.11006 Bull. Hell. Math. Soc. 60, 91-96 (2016). MSC: 11A07 PDFBibTeX XMLCite \textit{K. Smpokos}, Bull. Hell. Math. Soc. 60, 91--96 (2016; Zbl 1425.11006) Full Text: Link
Wei, Yangjiang; Su, Huadong; Tang, Gaohua Unit groups of quotient rings of complex quadratic rings. (English) Zbl 1348.05053 Front. Math. China 11, No. 4, 1037-1056 (2016). MSC: 05C05 11A07 13M05 PDFBibTeX XMLCite \textit{Y. Wei} et al., Front. Math. China 11, No. 4, 1037--1056 (2016; Zbl 1348.05053) Full Text: DOI
Lalín, Matilde N.; Rogers, Mathew D. Variations of the Ramanujan polynomials and remarks on \(\zeta(2j+1)/\pi^{2j+1}\). (English) Zbl 1272.26007 Funct. Approximatio, Comment. Math. 48, No. 1, 91-111 (2013). Reviewer: József Sándor (Cluj-Napoca) MSC: 26C10 11B68 PDFBibTeX XMLCite \textit{M. N. Lalín} and \textit{M. D. Rogers}, Funct. Approximatio, Comment. Math. 48, No. 1, 91--111 (2013; Zbl 1272.26007) Full Text: DOI arXiv Euclid
Adolphson, Alan; Sperber, Steven On unit root formulas for toric exponential sums. (English) Zbl 1251.11081 Algebra Number Theory 6, No. 3, 573-585 (2012). Reviewer: John H. Loxton (Greenwich, NSW) MSC: 11T23 11S40 11S80 PDFBibTeX XMLCite \textit{A. Adolphson} and \textit{S. Sperber}, Algebra Number Theory 6, No. 3, 573--585 (2012; Zbl 1251.11081) Full Text: DOI arXiv Link
Polak, Agnieszka Algorithms for integral solutions of a class of Diophantine equations. (English) Zbl 1318.11166 Control Cybern. 40, No. 2, 491-514 (2011). MSC: 11Y50 PDFBibTeX XMLCite \textit{A. Polak}, Control Cybern. 40, No. 2, 491--514 (2011; Zbl 1318.11166)
Qu, Yinchun; Li, Libin The residue class ring with structure of unit group being \(\mathbb Z_2\oplus \mathbb Z_{p^m}\). (Chinese. English summary) Zbl 1265.11002 J. Hubei Univ., Nat. Sci. 33, No. 4, 433-436 (2011). MSC: 11A07 13M05 20K01 PDFBibTeX XMLCite \textit{Y. Qu} and \textit{L. Li}, J. Hubei Univ., Nat. Sci. 33, No. 4, 433--436 (2011; Zbl 1265.11002)
Qu, Yinchun; Li, Libin The remainder classes ring with the order of unit group being \(2pq\). (Chinese. English summary) Zbl 1249.11005 J. Hubei Univ., Nat. Sci. 33, No. 1, 1-6 (2011). MSC: 11A07 13M05 20K01 PDFBibTeX XMLCite \textit{Y. Qu} and \textit{L. Li}, J. Hubei Univ., Nat. Sci. 33, No. 1, 1--6 (2011; Zbl 1249.11005)
Ayache, Ahmed; Echi, Othman; Naimi, Mongi On Kronecker polynomials. (English) Zbl 1235.11013 Rocky Mt. J. Math. 41, No. 3, 707-725 (2011). Reviewer: Pieter Moree (Bonn) MSC: 11A41 11A51 11C08 PDFBibTeX XMLCite \textit{A. Ayache} et al., Rocky Mt. J. Math. 41, No. 3, 707--725 (2011; Zbl 1235.11013) Full Text: DOI
Qu, Yinchun; Yang, Yichao; Li, Libin The remainder classes ring with unit group being the direct sum of prime order cycle groups. (Chinese. English summary) Zbl 1240.11004 J. Yangzhou Univ., Nat. Sci. Ed. 13, No. 3, 1-4 (2010). MSC: 11A07 13M05 20K01 PDFBibTeX XMLCite \textit{Y. Qu} et al., J. Yangzhou Univ., Nat. Sci. Ed. 13, No. 3, 1--4 (2010; Zbl 1240.11004)
Ramaswamy, H. N.; Siddaramu, R. On the stufe, unit stufe and Pythagoras number of the ring of integers modulo \(n\). (English) Zbl 1246.11089 Adv. Stud. Contemp. Math., Kyungshang 20, No. 3, 373-388 (2010). Reviewer: Kazimierz Szymiczek (Katowice) (MR2676906) MSC: 11E04 11A07 11E25 11E81 PDFBibTeX XMLCite \textit{H. N. Ramaswamy} and \textit{R. Siddaramu}, Adv. Stud. Contemp. Math., Kyungshang 20, No. 3, 373--388 (2010; Zbl 1246.11089)
Murty, M. Ram; Petersen, Kathleen L. The generalized Artin conjecture and arithmetic orbifolds. (English) Zbl 1230.11141 Harnad, John (ed.) et al., Groups and symmetries. From Neolithic Scots to John McKay. Selected papers of the conference, Montreal, Canada, April 27–29, 2007. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4481-6/pbk). CRM Proceedings and Lecture Notes 47, 259-265 (2009). Reviewer: Pieter Moree (Bonn) MSC: 11R47 11A07 11N36 11R44 PDFBibTeX XMLCite \textit{M. R. Murty} and \textit{K. L. Petersen}, in: Groups and symmetries. From Neolithic Scots to John McKay. Selected papers of the conference, Montreal, Canada, April 27--29, 2007. Providence, RI: American Mathematical Society (AMS). 259--265 (2009; Zbl 1230.11141)
Chapman, Robin; Pan, Hao \(q\)-analogues of Wilson’s theorem. (English) Zbl 1162.11004 Int. J. Number Theory 4, No. 4, 539-547 (2008). Reviewer: Le Maohua (Zhanjiang) MSC: 11A07 05A30 11R29 PDFBibTeX XMLCite \textit{R. Chapman} and \textit{H. Pan}, Int. J. Number Theory 4, No. 4, 539--547 (2008; Zbl 1162.11004) Full Text: DOI arXiv
Sun, Zhihong On the quadratic character of quadratic units. (English) Zbl 1137.11003 J. Number Theory 128, No. 5, 1295-1335 (2008). Reviewer: Pieter Moree (Bonn) MSC: 11A15 11B39 11A07 11E25 11E16 PDFBibTeX XMLCite \textit{Z. Sun}, J. Number Theory 128, No. 5, 1295--1335 (2008; Zbl 1137.11003) Full Text: DOI
Kuba, G. Several types of algebraic numbers on the unit circle. (English) Zbl 1075.11064 Arch. Math. 85, No. 1, 70-78 (2005). Reviewer: Artūras Dubickas (Vilnius) MSC: 11R04 11R09 PDFBibTeX XMLCite \textit{G. Kuba}, Arch. Math. 85, No. 1, 70--78 (2005; Zbl 1075.11064) Full Text: DOI
Kurlberg, Pär On the order of unimodular matrices modulo integers. (English) Zbl 1030.11048 Acta Arith. 110, No. 2, 141-151 (2003). Reviewer: Pieter Moree (Amsterdam) MSC: 11N37 11A07 PDFBibTeX XMLCite \textit{P. Kurlberg}, Acta Arith. 110, No. 2, 141--151 (2003; Zbl 1030.11048) Full Text: DOI arXiv
Laššák, Miroslav Bauer’s congruence in algebraic number fields. (English) Zbl 1088.11077 Tatra Mt. Math. Publ. 20, 143-154 (2000). MSC: 11R04 11A07 PDFBibTeX XMLCite \textit{M. Laššák}, Tatra Mt. Math. Publ. 20, 143--154 (2000; Zbl 1088.11077)
Esmonde, Jody; Murty, M. Ram Problems in algebraic number theory. (English) Zbl 0911.11001 Graduate Texts in Mathematics. 190. New York, NY: Springer. xiv, 314 p. (1999). Reviewer: Franz Lemmermeyer (Saarbrücken) MSC: 11-01 00A07 11A05 11A07 11R04 11R27 11R11 11R29 11N13 PDFBibTeX XMLCite \textit{J. Esmonde} and \textit{M. R. Murty}, Problems in algebraic number theory. New York, NY: Springer (1999; Zbl 0911.11001)
Dräxler, P.; Golovachtchuk, N.; Ovsienko, S.; de la Peña, J. A. Coordinates of maximal roots of weakly non-negative unit forms. (English) Zbl 0936.16011 Colloq. Math. 78, No. 2, 163-193 (1998). Reviewer: S.Kasjan (Toruń) MSC: 16G20 16G60 15A63 17B67 11E12 PDFBibTeX XMLCite \textit{P. Dräxler} et al., Colloq. Math. 78, No. 2, 163--193 (1998; Zbl 0936.16011) Full Text: DOI EuDML
Jones, Gareth A.; Jones, Josephine Mary Elementary number theory. (English) Zbl 0891.11001 Springer Undergraduate Mathematics Series. Berlin: Springer. xiv, 301 p. (1998). Reviewer: J.H.Loxton (North Ryde) MSC: 11-01 11M06 11Axx 11M26 11D41 PDFBibTeX XMLCite \textit{G. A. Jones} and \textit{J. M. Jones}, Elementary number theory. Berlin: Springer (1998; Zbl 0891.11001) Full Text: DOI
de la Peña, J. A. The Tits form of a tame algebra. (English) Zbl 0849.16012 Bautista, Raymundo (ed.) et al., Representation theory of algebras and related topics. Proceedings of the workshop, Mexico City, Mexico, August 16-20, 1994. Providence, RI: American Mathematical Society. CMS Conf. Proc. 19, 159-183 (1996). MSC: 16G20 16G60 16G70 11E04 PDFBibTeX XMLCite \textit{J. A. de la Peña}, CMS Conf. Proc. 19, 159--183 (1996; Zbl 0849.16012)
Zannier, Umberto Vanishing sums of roots of unity. (English) Zbl 0891.11015 Rend. Semin. Mat., Torino 53, No. 4, 487-495 (1995). Reviewer: J.H.Loxton (North Ryde) MSC: 11D61 11R18 PDFBibTeX XMLCite \textit{U. Zannier}, Rend. Semin. Mat., Torino 53, No. 4, 487--495 (1995; Zbl 0891.11015)
Young, Paul Thomas Apéry numbers, Jacobi sums, and special values of generalized \(p\)-adic hypergeometric functions. (English) Zbl 0759.11042 J. Number Theory 41, No. 2, 231-255 (1992). Reviewer: F.Beukers (Utrecht) MSC: 11S80 33C20 12H25 11S40 PDFBibTeX XMLCite \textit{P. T. Young}, J. Number Theory 41, No. 2, 231--255 (1992; Zbl 0759.11042) Full Text: DOI
Yang, Po On the number of solutions of the congruence \(\sum^ k_{i=1} x^ 2_ i \equiv{}0\pmod p( 1 \leq x_ 1 <x_ 2 <\dots <x_ k \leq(p-1)/2)\). (Chinese. English summary) Zbl 0768.11002 J. Sichuan Univ., Nat. Sci. Ed. 29, No. 1, 8-15 (1992). Reviewer: Ke Zhao (Chengdu) MSC: 11A07 11R29 11R11 PDFBibTeX XMLCite \textit{P. Yang}, J. Sichuan Univ., Nat. Sci. Ed. 29, No. 1, 8--15 (1992; Zbl 0768.11002)
Endô, Akira Class number relation between certain sextic number fields. (English) Zbl 0583.12003 Proc. Am. Math. Soc. 95, 199-204 (1985). Reviewer: C.Parry MSC: 11R23 11R18 11R21 PDFBibTeX XMLCite \textit{A. Endô}, Proc. Am. Math. Soc. 95, 199--204 (1985; Zbl 0583.12003) Full Text: DOI
Gallian, Joseph A.; Rusin, David J. Factoring groups of integers modulo n. (English) Zbl 0426.10002 Math. Mag. 53, 33-36 (1980). MSC: 11A07 PDFBibTeX XMLCite \textit{J. A. Gallian} and \textit{D. J. Rusin}, Math. Mag. 53, 33--36 (1980; Zbl 0426.10002) Full Text: DOI
Cohen, Eckford The definitions of the Euler and Möbius functions. (English) Zbl 0124.02703 Math. Mag. 38, 14-17 (1965). Reviewer: Wilfried Nöbauer (Wien) MSC: 11A25 PDFBibTeX XMLCite \textit{E. Cohen}, Math. Mag. 38, 14--17 (1965; Zbl 0124.02703) Full Text: DOI
Brandt, Heinrich Über das quadratische Reziprozitätsgesetz im Körper der dritten Einheitswurzeln. (German) Zbl 0048.27303 Nova Acta Leopoldina, n. F. 15, 165-188 (1952). Reviewer: Mikao Moriya (Sapporo) MSC: 11A15 11R18 PDFBibTeX XML
Hensel, Kurt Multiplicative representation of algebraic numbers for the range of an arbitrary prime divisor. (Die multiplikative Darstellung der algebraischen Zahlen für den Bereich eines beliebigen Primteilers.) (German) JFM 46.0251.01 J. Reine Angew. Math. 146, 189-215 (1916). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11S15 11S99 PDFBibTeX XMLCite \textit{K. Hensel}, J. Reine Angew. Math. 146, 189--215 (1916; JFM 46.0251.01) Full Text: Crelle EuDML
Western, A. E. Some criteria for the residues of eighth and other powers. (English) JFM 42.0233.01 Proc. Lond. Math. Soc. (2) 9, 244-272 (1911). Reviewer: Fueter, Prof. (Karlsruhe) MSC: 11A15 PDFBibTeX XMLCite \textit{A. E. Western}, Proc. Lond. Math. Soc. (2) 9, 244--272 (1911; JFM 42.0233.01) Full Text: DOI Link