Bayad, Abdelmejid; Seddik, Mohammed Index, the prime ideal factorization in simplest quartic fields and counting their discriminants. (English) Zbl 1499.11314 Filomat 34, No. 2, 591-600 (2020). MSC: 11R04 11R16 11R27 11R29 11R42 PDFBibTeX XMLCite \textit{A. Bayad} and \textit{M. Seddik}, Filomat 34, No. 2, 591--600 (2020; Zbl 1499.11314) Full Text: DOI
Zhang, Yong; Shamsi Zargar, Arman Integral triangles and perpendicular quadrilateral pairs with a common area and a common perimeter. (English) Zbl 1473.11125 Funct. Approximatio, Comment. Math. 63, No. 2, 165-180 (2020). MSC: 11G05 11D25 11D72 51M05 51M25 PDFBibTeX XMLCite \textit{Y. Zhang} and \textit{A. Shamsi Zargar}, Funct. Approximatio, Comment. Math. 63, No. 2, 165--180 (2020; Zbl 1473.11125) Full Text: DOI
Colliot-Thélène, Jean-Louis; Wei, Dasheng; Xu, Fei Brauer-Manin obstruction for Markoff surfaces. (English) Zbl 1478.11091 Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 21, Spec. Iss., 1257-1313 (2020). Reviewer: B. Z. Moroz (Bonn) MSC: 11G35 11D25 14F22 PDFBibTeX XMLCite \textit{J.-L. Colliot-Thélène} et al., Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 21, 1257--1313 (2020; Zbl 1478.11091) Full Text: DOI arXiv
Kodera, Yuta; Duquesne, Sylvain; Nogami, Yasuyuki Multiplication and squaring in cubic and quartic extensions for pairing based cryptography. (English) Zbl 07358950 Davis, James A. (ed.), Finite fields and their applications. Proceedings of the 14th international conference on finite fields and their applications (Fq14), Vancouver, Canada, June 3–7, 2019. Berlin: De Gruyter. De Gruyter Proc. Math., 71-86 (2020). Reviewer: Alessandro Neri (Ghent) MSC: 11T71 94A60 PDFBibTeX XMLCite \textit{Y. Kodera} et al., in: Finite fields and their applications. Proceedings of the 14th international conference on finite fields and their applications (Fq14), Vancouver, Canada, June 3--7, 2019. Berlin: De Gruyter. 71--86 (2020; Zbl 07358950) Full Text: DOI
El Fadil, Lhoussain On power integral bases for certain pure number fields defined by \(x^{24}-m\). (English) Zbl 1474.11182 Stud. Sci. Math. Hung. 57, No. 3, 397-407 (2020). Reviewer: István Gaál (Debrecen) MSC: 11R04 11R16 11R21 PDFBibTeX XMLCite \textit{L. El Fadil}, Stud. Sci. Math. Hung. 57, No. 3, 397--407 (2020; Zbl 1474.11182) Full Text: DOI
Gaiko, Valery A. Global bifurcations of limit cycles in an endocrine system model. (English) Zbl 1454.34050 Adv. Dyn. Syst. Appl. 15, No. 1, 15-25 (2020). MSC: 34C05 34C07 34C23 37G05 37G10 37G15 PDFBibTeX XMLCite \textit{V. A. Gaiko}, Adv. Dyn. Syst. Appl. 15, No. 1, 15--25 (2020; Zbl 1454.34050) Full Text: Link
Das, Shamik; Saikia, Anupam Families of non-congruent numbers with arbitrarily many pairs of prime factors. (English) Zbl 1459.11085 Integers 20, Paper A55, 12 p. (2020). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11D25 11G05 14G05 14H25 PDFBibTeX XMLCite \textit{S. Das} and \textit{A. Saikia}, Integers 20, Paper A55, 12 p. (2020; Zbl 1459.11085) Full Text: Link
Aouissi, S.; Mayer, D. C.; Ismaili, M. C.; Talbi, M.; Azizi, A. 3-rank of ambiguous class groups of cubic Kummer extensions. (English) Zbl 1474.11186 Period. Math. Hung. 81, No. 2, 250-274 (2020). MSC: 11R11 11R16 11R20 11R27 11R29 11R37 PDFBibTeX XMLCite \textit{S. Aouissi} et al., Period. Math. Hung. 81, No. 2, 250--274 (2020; Zbl 1474.11186) Full Text: DOI arXiv
Zhang, Yong; Shen, Zhongyan Arithmetic properties of polynomials. (English) Zbl 1474.11088 Period. Math. Hung. 81, No. 1, 134-148 (2020). MSC: 11D25 11D72 11G05 PDFBibTeX XMLCite \textit{Y. Zhang} and \textit{Z. Shen}, Period. Math. Hung. 81, No. 1, 134--148 (2020; Zbl 1474.11088) Full Text: DOI arXiv
Louboutin, Stéphane R. When is the order generated by a cubic, quartic or quintic algebraic unit Galois invariant: three conjectures. (English) Zbl 1524.11201 Czech. Math. J. 70, No. 4, 905-919 (2020). Reviewer: Claude Levesque (Québec) MSC: 11R27 11R16 11R20 PDFBibTeX XMLCite \textit{S. R. Louboutin}, Czech. Math. J. 70, No. 4, 905--919 (2020; Zbl 1524.11201) Full Text: DOI
Bremner, Andrew; Choudhry, Ajai The Fermat cubic and quartic curves over cyclic fields. (English) Zbl 1474.14041 Period. Math. Hung. 80, No. 2, 147-157 (2020). MSC: 14G25 11D25 11G05 PDFBibTeX XMLCite \textit{A. Bremner} and \textit{A. Choudhry}, Period. Math. Hung. 80, No. 2, 147--157 (2020; Zbl 1474.14041) Full Text: DOI
H, Piper; Harron, Robert The shapes of Galois quartic fields. (English) Zbl 1462.11097 Trans. Am. Math. Soc. 373, No. 10, 7109-7152 (2020). Reviewer: Robert W. van der Waall (Amsterdam) MSC: 11R16 11R45 11E12 11P21 11H06 15A03 52C05 PDFBibTeX XMLCite \textit{P. H} and \textit{R. Harron}, Trans. Am. Math. Soc. 373, No. 10, 7109--7152 (2020; Zbl 1462.11097) Full Text: DOI arXiv
Ishitsuka, Yasuhiro; Ito, Tetsushi; Ohshita, Tatsuya; Taniguchi, Takashi; Uchida, Yukihiro The local-global property for bitangents of plane quartics. (English) Zbl 1448.14023 JSIAM Lett. 12, 41-44 (2020). MSC: 14H25 14J20 14J42 11G35 PDFBibTeX XMLCite \textit{Y. Ishitsuka} et al., JSIAM Lett. 12, 41--44 (2020; Zbl 1448.14023) Full Text: DOI arXiv
An, Chen \(\ell\)-torsion in class groups of certain families of \(D_4\)-quartic fields. (English. French summary) Zbl 1453.11136 J. Théor. Nombres Bordx. 32, No. 1, 1-23 (2020). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R16 11R29 PDFBibTeX XMLCite \textit{C. An}, J. Théor. Nombres Bordx. 32, No. 1, 1--23 (2020; Zbl 1453.11136) Full Text: DOI arXiv
Llibre, Jaume; Martínez, Paulina; Vidal, Claudio Limit cycles of a perturbation of a polynomial Hamiltonian systems of degree 4 symmetric with respect to the origin. (English) Zbl 1451.34033 Can. Math. Bull. 63, No. 3, 547-561 (2020). MSC: 34C07 34C08 34E10 PDFBibTeX XMLCite \textit{J. Llibre} et al., Can. Math. Bull. 63, No. 3, 547--561 (2020; Zbl 1451.34033) Full Text: DOI
Zili, M.; Zougar, E. Exact variations for stochastic heat equations with piecewise constant coefficients and application to parameter estimation. (English) Zbl 1454.60100 Theory Probab. Math. Stat. 100, 77-106 (2020) and Teor. Jmovirn. Mat. Stat. 100, 75-101 (2019). Reviewer: Udhayakumar Ramalingam (Vellore) MSC: 60H15 60G15 60G17 35R05 60G60 35K10 33B20 62F10 PDFBibTeX XMLCite \textit{M. Zili} and \textit{E. Zougar}, Theory Probab. Math. Stat. 100, 77--106 (2020; Zbl 1454.60100) Full Text: DOI
Li, Yangcheng; Zhang, Yong \(\theta\)-triangle and \(\omega\)-parallelogram pairs with areas and perimeters in certain proportions. (English) Zbl 1440.51006 Rocky Mt. J. Math. 50, No. 3, 1059-1071 (2020). MSC: 51M25 11D25 11G05 51M05 PDFBibTeX XMLCite \textit{Y. Li} and \textit{Y. Zhang}, Rocky Mt. J. Math. 50, No. 3, 1059--1071 (2020; Zbl 1440.51006) Full Text: DOI Euclid
Aouissi, Siham; Talbi, Mohamed; Ismaili, Moulay Chrif; Azizi, Abdelmalek On a conjecture of Lemmermeyer. (English) Zbl 1481.11106 Int. J. Number Theory 16, No. 7, 1407-1424 (2020). Reviewer: Robert W. van der Waall (Huizen) MSC: 11R11 11R16 11R20 11R27 11R29 11R37 PDFBibTeX XMLCite \textit{S. Aouissi} et al., Int. J. Number Theory 16, No. 7, 1407--1424 (2020; Zbl 1481.11106) Full Text: DOI arXiv
Zhang, Yong; Shamsi Zargar, Arman On the Diophantine equations \(z^2=f(x)^2 \pm f(y)^2\) involving Laurent polynomials. (English) Zbl 1450.11029 Funct. Approximatio, Comment. Math. 62, No. 2, 187-201 (2020). Reviewer: Maciej Ulas (Kraków) MSC: 11D72 11D25 11D41 11G05 PDFBibTeX XMLCite \textit{Y. Zhang} and \textit{A. Shamsi Zargar}, Funct. Approximatio, Comment. Math. 62, No. 2, 187--201 (2020; Zbl 1450.11029) Full Text: DOI arXiv Euclid
Srinivas, Kotyada; Subramani, Muthukrishnan A survey of certain Euclidean number fields. (English) Zbl 1436.11127 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. 57-65 (2020). MSC: 11R04 11A05 11R16 11-02 PDFBibTeX XMLCite \textit{K. Srinivas} and \textit{M. Subramani}, in: 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. 57--65 (2020; Zbl 1436.11127) Full Text: DOI
Hu, Guangwei; Wang, Ke Higher moment of coefficients of Dedekind zeta function. (English) Zbl 1466.11087 Front. Math. China 15, No. 1, 57-67 (2020). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R42 11E25 11F30 11N37 11R16 PDFBibTeX XMLCite \textit{G. Hu} and \textit{K. Wang}, Front. Math. China 15, No. 1, 57--67 (2020; Zbl 1466.11087) Full Text: DOI
Ishitsuka, Yasuhiro; Ito, Tetsushi; Ohshita, Tatsuya Explicit calculation of the mod 4 Galois representation associated with the Fermat quartic. (English) Zbl 1491.11065 Int. J. Number Theory 16, No. 4, 881-905 (2020). MSC: 11G25 11D41 11F80 11G10 14H50 14K15 14K30 PDFBibTeX XMLCite \textit{Y. Ishitsuka} et al., Int. J. Number Theory 16, No. 4, 881--905 (2020; Zbl 1491.11065) Full Text: DOI arXiv
Umegaki, Atsuki; Umegaki, Yumiko Quartic fields with large class numbers. (English) Zbl 1448.11201 Rocky Mt. J. Math. 50, No. 1, 267-280 (2020). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R29 11R16 PDFBibTeX XMLCite \textit{A. Umegaki} and \textit{Y. Umegaki}, Rocky Mt. J. Math. 50, No. 1, 267--280 (2020; Zbl 1448.11201) Full Text: DOI Euclid
Doran, Charles F.; Kelly, Tyler L.; Salerno, Adriana; Sperber, Steven; Voight, John; Whitcher, Ursula Hypergeometric decomposition of symmetric \(K3\) quartic pencils. (English) Zbl 1441.14128 Res. Math. Sci. 7, No. 2, Paper No. 7, 81 p. (2020). Reviewer: Noriko Yui (Kingston) MSC: 14J28 14Q10 33C05 33D67 PDFBibTeX XMLCite \textit{C. F. Doran} et al., Res. Math. Sci. 7, No. 2, Paper No. 7, 81 p. (2020; Zbl 1441.14128) Full Text: DOI arXiv
Shamsi Zargar, Arman On the rank of elliptic curves arising from Pythagorean quadruplets. (English) Zbl 1441.14108 Kodai Math. J. 43, No. 1, 129-142 (2020). Reviewer: Andrea Bandini (Pisa) MSC: 11G05 11D25 11D09 14H52 PDFBibTeX XMLCite \textit{A. Shamsi Zargar}, Kodai Math. J. 43, No. 1, 129--142 (2020; Zbl 1441.14108) Full Text: DOI Euclid
Aoki, Miho; Kishi, Yasuhiro A family of pairs of imaginary cyclic fields of degree \((p-1)/2\) with both class numbers divisible by \(p\). (English) Zbl 1447.11113 Ramanujan J. 52, No. 1, 133-161 (2020). Reviewer: James E. Carter (Charleston) MSC: 11R11 11R16 11R29 PDFBibTeX XMLCite \textit{M. Aoki} and \textit{Y. Kishi}, Ramanujan J. 52, No. 1, 133--161 (2020; Zbl 1447.11113) Full Text: DOI arXiv
Tian, Yuzhou; Zhao, Yulin Global phase portraits and bifurcation diagrams for Hamiltonian systems of linear plus quartic homogeneous polynomials symmetric with respect to the \(y\)-axis. (English) Zbl 1442.37070 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 192, Article ID 111658, 27 p. (2020). Reviewer: Cristian Lăzureanu (Timisoara) MSC: 37J20 70K05 70H33 34C05 34C07 PDFBibTeX XMLCite \textit{Y. Tian} and \textit{Y. Zhao}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 192, Article ID 111658, 27 p. (2020; Zbl 1442.37070) Full Text: DOI
Cerbu, Alois; Gunther, Elijah; Magee, Michael; Peilen, Luke The cycle structure of a Markoff automorphism over finite fields. (English) Zbl 1459.37096 J. Number Theory 211, 1-27 (2020). MSC: 37P05 37P35 11D25 11G35 11F06 20B27 11G20 PDFBibTeX XMLCite \textit{A. Cerbu} et al., J. Number Theory 211, 1--27 (2020; Zbl 1459.37096) Full Text: DOI arXiv Link
Katsipis, Nikos Diophantine equations coming from binomial near-collisions. (English) Zbl 1432.11034 Integers 20, Paper A13, 15 p. (2020). MSC: 11D25 11G05 11B65 PDFBibTeX XMLCite \textit{N. Katsipis}, Integers 20, Paper A13, 15 p. (2020; Zbl 1432.11034) Full Text: arXiv Link
Drungilas, Paulius; Dubickas, Arturas Reducibility of polynomials after a polynomial substitution. (English) Zbl 1449.12001 Publ. Math. Debr. 96, No. 1-2, 185-194 (2020). Reviewer: Piroska Lakatos (Debrecen) MSC: 12D05 11D25 11D61 PDFBibTeX XMLCite \textit{P. Drungilas} and \textit{A. Dubickas}, Publ. Math. Debr. 96, No. 1--2, 185--194 (2020; Zbl 1449.12001) Full Text: DOI
Zhang, Yong; Chen, Deyi A Diophantine equation with the harmonic mean. (English) Zbl 1449.11070 Period. Math. Hung. 46, No. 1, 138-144 (2020). Reviewer: Thomas A. Schmidt (Corvallis) MSC: 11D72 11D25 11D41 11G05 PDFBibTeX XMLCite \textit{Y. Zhang} and \textit{D. Chen}, Period. Math. Hung. 46, No. 1, 138--144 (2020; Zbl 1449.11070) Full Text: DOI
Gao, Peng; Zhao, Liangyi Moments of central values of cubic Hecke \(L\)-functions of \(\mathbb{Q}(i)\). (English) Zbl 1487.11080 Res. Number Theory 6, No. 1, Paper No. 14, 22 p. (2020). Reviewer: Maciej Radziejewski (Poznań) MSC: 11L40 11R16 11R42 PDFBibTeX XMLCite \textit{P. Gao} and \textit{L. Zhao}, Res. Number Theory 6, No. 1, Paper No. 14, 22 p. (2020; Zbl 1487.11080) Full Text: DOI arXiv
Azizi, Abdelmalek; Zekhnini, Abdelkader; Taous, Mohammed On the capitulation of the 2-ideal classes of the field \(\mathbb{Q}(\sqrt{p_1p_2q},i)\) of type \((2,2,2)\). (English) Zbl 1431.11118 Bol. Soc. Parana. Mat. (3) 38, No. 4, 127-135 (2020). MSC: 11R11 11R16 11R20 11R27 11R29 PDFBibTeX XMLCite \textit{A. Azizi} et al., Bol. Soc. Parana. Mat. (3) 38, No. 4, 127--135 (2020; Zbl 1431.11118) Full Text: Link
Hough, Robert D. The local zeta function in enumerating quartic fields. (English) Zbl 1454.11175 J. Number Theory 210, 1-131 (2020). MSC: 11N45 11R16 11S90 11T23 PDFBibTeX XMLCite \textit{R. D. Hough}, J. Number Theory 210, 1--131 (2020; Zbl 1454.11175) Full Text: DOI arXiv
Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen Reconstructing plane quartics from their invariants. (English) Zbl 1439.13020 Discrete Comput. Geom. 63, No. 1, 73-113 (2020). Reviewer: Peter Schenzel (Halle) MSC: 13A50 14L24 14H10 14H25 PDFBibTeX XMLCite \textit{R. Lercier} et al., Discrete Comput. Geom. 63, No. 1, 73--113 (2020; Zbl 1439.13020) Full Text: DOI arXiv
da Cruz, Leonardo P. C.; Romanovski, Valery G.; Torregrosa, J. The center and cyclicity problems for quartic linear-like reversible systems. (English) Zbl 1446.34046 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 190, Article ID 111593, 19 p. (2020). Reviewer: Alexander Rudenok (Minsk) MSC: 34C05 34C07 34C23 34C25 34C14 PDFBibTeX XMLCite \textit{L. P. C. da Cruz} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 190, Article ID 111593, 19 p. (2020; Zbl 1446.34046) Full Text: DOI Link
Gallegos-Ruiz, H. R.; Katsipis, N.; Tengely, Sz.; Ulas, M. On the Diophantine equation \(\binom{n}{k} = \binom{m}{l} + d\). (English) Zbl 1451.11020 J. Number Theory 208, 418-440 (2020). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11D25 11D41 11G30 11G05 11J86 PDFBibTeX XMLCite \textit{H. R. Gallegos-Ruiz} et al., J. Number Theory 208, 418--440 (2020; Zbl 1451.11020) Full Text: DOI arXiv
Louboutin, Stéphane R. Non-Galois cubic number fields with exceptional units. II. (English) Zbl 1453.11137 J. Number Theory 206, 62-80 (2020). MSC: 11R16 11R27 PDFBibTeX XMLCite \textit{S. R. Louboutin}, J. Number Theory 206, 62--80 (2020; Zbl 1453.11137) Full Text: DOI
Alpöge, Levent; Bhargava, Manjul; Shnidman, Ari A positive proportion of cubic fields are not monogenic yet have no local obstruction to being so. arXiv:2011.01186 Preprint, arXiv:2011.01186 [math.NT] (2020). MSC: 11R16 11R45 11G05 BibTeX Cite \textit{L. Alpöge} et al., ``A positive proportion of cubic fields are not monogenic yet have no local obstruction to being so'', Preprint, arXiv:2011.01186 [math.NT] (2020) Full Text: arXiv OA License
Doležálek, Matěj Quaternions and universal quadratic forms over number fields. arXiv:2012.07097 Preprint, arXiv:2012.07097 [math.NT] (2020). MSC: 11E12 11H06 11R52 11R80 11R16 BibTeX Cite \textit{M. Doležálek}, ``Quaternions and universal quadratic forms over number fields'', Preprint, arXiv:2012.07097 [math.NT] (2020) Full Text: arXiv OA License