Zhao, Junyong; Feng, Yulu; Hong, Shaofang; Zhu, Chaoxi On the number of zeros of diagonal quartic forms over finite fields. (English) Zbl 07502652 Forum Math. 34, No. 2, 385-405 (2022). MSC: 11T06 11T22 PDF BibTeX XML Cite \textit{J. Zhao} et al., Forum Math. 34, No. 2, 385--405 (2022; Zbl 07502652) Full Text: DOI OpenURL
Cao, Wei \(p\)-adic valuations associated to fibers and images of polynomial functions. (English) Zbl 07432413 Finite Fields Appl. 77, Article ID 101951, 12 p. (2022). Reviewer: Telveenus Antony (Kingston upon Thames) MSC: 11T24 11T06 PDF BibTeX XML Cite \textit{W. Cao}, Finite Fields Appl. 77, Article ID 101951, 12 p. (2022; Zbl 07432413) Full Text: DOI OpenURL
Hong, Shaofang; Zhu, Chaoxi On the number of zeros of diagonal cubic forms over finite fields. (English) Zbl 07509474 Forum Math. 33, No. 3, 697-708 (2021). MSC: 11T23 11T24 PDF BibTeX XML Cite \textit{S. Hong} and \textit{C. Zhu}, Forum Math. 33, No. 3, 697--708 (2021; Zbl 07509474) Full Text: DOI OpenURL
Clark, Pete L.; Genao, Tyler; Saia, Frederick Chevalley-Warning at the boundary. (English) Zbl 07432163 Expo. Math. 39, No. 4, 604-623 (2021). Reviewer: Telveenus Antony (Kingston upon Thames) MSC: 11T06 11D79 PDF BibTeX XML Cite \textit{P. L. Clark} et al., Expo. Math. 39, No. 4, 604--623 (2021; Zbl 07432163) Full Text: DOI OpenURL
Zhu, Chaoxi; Feng, Yulu; Hong, Shaofang; Zhao, Junyong On the number of zeros to the equation \(f(x_1)+\cdots+f(x_n)=a\) over finite fields. (English) Zbl 1484.11222 Finite Fields Appl. 76, Article ID 101922, 16 p. (2021). MSC: 11T23 11T24 PDF BibTeX XML Cite \textit{C. Zhu} et al., Finite Fields Appl. 76, Article ID 101922, 16 p. (2021; Zbl 1484.11222) Full Text: DOI arXiv OpenURL
Blache, Régis Hasse-Witt matrices for polynomials, and applications. (English) Zbl 1479.11157 Rend. Semin. Mat. Univ. Padova 145, 117-152 (2021). MSC: 11M38 11T23 14G15 11G25 PDF BibTeX XML Cite \textit{R. Blache}, Rend. Semin. Mat. Univ. Padova 145, 117--152 (2021; Zbl 1479.11157) Full Text: DOI OpenURL
Aichinger, Erhard; Moosbauer, Jakob Chevalley-Warning type results on abelian groups. (English) Zbl 07286476 J. Algebra 569, 30-66 (2021). MSC: 20K01 13F20 20C05 PDF BibTeX XML Cite \textit{E. Aichinger} and \textit{J. Moosbauer}, J. Algebra 569, 30--66 (2021; Zbl 07286476) Full Text: DOI arXiv OpenURL
Castro, Francis N.; Moreno, Oscar; Rubio, Ivelisse An improvement of a theorem of Carlitz. (English) Zbl 1473.11216 J. Pure Appl. Algebra 224, No. 5, Article ID 106246, 7 p. (2020). Reviewer: Lekbir Chakri (Rabat) MSC: 11T06 11G25 PDF BibTeX XML Cite \textit{F. N. Castro} et al., J. Pure Appl. Algebra 224, No. 5, Article ID 106246, 7 p. (2020; Zbl 1473.11216) Full Text: DOI OpenURL
Baoulina, Ioulia N.; Bishnoi, Anurag; Clark, Pete L. A generalization of the theorems of Chevalley-Warning and Ax-Katz via polynomial substitutions. (English) Zbl 1472.11294 Proc. Am. Math. Soc. 147, No. 10, 4107-4122 (2019). MSC: 11T06 11D79 11G25 PDF BibTeX XML Cite \textit{I. N. Baoulina} et al., Proc. Am. Math. Soc. 147, No. 10, 4107--4122 (2019; Zbl 1472.11294) Full Text: DOI arXiv OpenURL
Baoulina, Ioulia N. On a theorem of Morlaye and Joly and its generalization. (English) Zbl 1454.11215 Eur. J. Comb. 80, 37-42 (2019). MSC: 11T06 05C15 11D79 PDF BibTeX XML Cite \textit{I. N. Baoulina}, Eur. J. Comb. 80, 37--42 (2019; Zbl 1454.11215) Full Text: DOI arXiv OpenURL
Clark, Pete L.; Watson, Lori D. Varga’s theorem in number fields. (English) Zbl 1452.11145 Integers 18, Paper A74, 11 p. (2018). Reviewer: Robert Fitzgerald (Carbondale) MSC: 11T06 11R04 PDF BibTeX XML Cite \textit{P. L. Clark} and \textit{L. D. Watson}, Integers 18, Paper A74, 11 p. (2018; Zbl 1452.11145) Full Text: Link OpenURL
Clark, Pete L. Warning’s second theorem with relaxed outputs. (English) Zbl 1440.11225 J. Algebr. Comb. 48, No. 2, 325-349 (2018). MSC: 11T06 11B75 11D79 PDF BibTeX XML Cite \textit{P. L. Clark}, J. Algebr. Comb. 48, No. 2, 325--349 (2018; Zbl 1440.11225) Full Text: DOI OpenURL
Asgarli, Shamil A new proof of Warning’s second theorem. (English) Zbl 1431.11128 Am. Math. Mon. 125, No. 6, 549-553 (2018). MSC: 11T06 51E30 PDF BibTeX XML Cite \textit{S. Asgarli}, Am. Math. Mon. 125, No. 6, 549--553 (2018; Zbl 1431.11128) Full Text: DOI OpenURL
Gubarev, Vsevolod Yur’evich Rota-Baxter operators of weight zero on simple Jordan algebra of Clifford type. (English) Zbl 1432.17037 Sib. Èlektron. Mat. Izv. 14, 1524-1532 (2017). MSC: 17C20 15A66 17B38 PDF BibTeX XML Cite \textit{V. Y. Gubarev}, Sib. Èlektron. Mat. Izv. 14, 1524--1532 (2017; Zbl 1432.17037) Full Text: DOI arXiv OpenURL
Zhu, Hui June On a theorem of Ax and Katz. (English. French summary) Zbl 1416.11103 J. Théor. Nombres Bordx. 29, No. 1, 137-150 (2017). MSC: 11G25 14G15 PDF BibTeX XML Cite \textit{H. J. Zhu}, J. Théor. Nombres Bordx. 29, No. 1, 137--150 (2017; Zbl 1416.11103) Full Text: DOI arXiv OpenURL
Ivanyos, Gábor; Santha, Miklos Solving systems of diagonal polynomial equations over finite fields. (English) Zbl 1356.68281 Theor. Comput. Sci. 657, Part A, 73-85 (2017). MSC: 68W30 12Y05 68Q12 PDF BibTeX XML Cite \textit{G. Ivanyos} and \textit{M. Santha}, Theor. Comput. Sci. 657, Part A, 73--85 (2017; Zbl 1356.68281) Full Text: DOI OpenURL
Alahmadi, Adel N.; Glynn, David G. Multiple Hamilton cycles in bipartite cubic graphs: an algebraic method. (English) Zbl 1352.05103 Finite Fields Appl. 44, 18-21 (2017). MSC: 05C45 94B05 14G15 51E99 PDF BibTeX XML Cite \textit{A. N. Alahmadi} and \textit{D. G. Glynn}, Finite Fields Appl. 44, 18--21 (2017; Zbl 1352.05103) Full Text: DOI OpenURL
Casolo, Carlo; Dolfi, Silvio; Pacifici, Emanuele; Sanus, Lucia Groups whose character degree graph has diameter three. (English) Zbl 1398.20010 Isr. J. Math. 215, No. 2, 523-558 (2016). MSC: 20C15 20D60 05C25 05E15 20D10 20D20 PDF BibTeX XML Cite \textit{C. Casolo} et al., Isr. J. Math. 215, No. 2, 523--558 (2016; Zbl 1398.20010) Full Text: DOI arXiv OpenURL
Ivanyos, Gábor; Santha, Miklos On solving systems of diagonal polynomial equations over finite fields. (English) Zbl 1356.68280 Wang, Jianxin (ed.) et al., Frontiers in algorithmics. 9th international workshop, FAW 2015, Guilin, China, July 3–5, 2015. Proceedings. Cham: Springer (ISBN 978-3-319-19646-6/pbk; 978-3-319-19647-3/ebook). Lecture Notes in Computer Science 9130, 125-137 (2015). MSC: 68W30 12Y05 68Q12 PDF BibTeX XML Cite \textit{G. Ivanyos} and \textit{M. Santha}, Lect. Notes Comput. Sci. 9130, 125--137 (2015; Zbl 1356.68280) Full Text: DOI arXiv Link OpenURL
Lachaud, Gilles; Rolland, Robert On the number of points of algebraic sets over finite fields. (English. French summary) Zbl 1408.14088 J. Pure Appl. Algebra 219, No. 11, 5117-5136 (2015). MSC: 14G15 14G05 PDF BibTeX XML Cite \textit{G. Lachaud} and \textit{R. Rolland}, J. Pure Appl. Algebra 219, No. 11, 5117--5136 (2015; Zbl 1408.14088) Full Text: DOI arXiv OpenURL
Spencer, Craig V.; Wooley, Trevor D. Diophantine inequalities and quasi-algebraically closed fields. (English) Zbl 1308.11043 Isr. J. Math. 191, Part B, 721-738 (2012). Reviewer: Scott T. Parsell (West Chester) MSC: 11D75 11J25 11T55 12F20 11E10 PDF BibTeX XML Cite \textit{C. V. Spencer} and \textit{T. D. Wooley}, Isr. J. Math. 191, Part B, 721--738 (2012; Zbl 1308.11043) Full Text: DOI arXiv OpenURL
Katz, Daniel J. On theorems of Delsarte-McEliece and Chevalley-Warning-Ax-Katz. (English) Zbl 1272.94091 Des. Codes Cryptography 65, No. 3, 291-324 (2012). Reviewer: Nathan Kaplan (New Haven) MSC: 94B15 11T71 11T06 PDF BibTeX XML Cite \textit{D. J. Katz}, Des. Codes Cryptography 65, No. 3, 291--324 (2012; Zbl 1272.94091) Full Text: DOI OpenURL
Blache, Régis Valuation of exponential sums and the generic first slope for Artin-Schreier curves. (English) Zbl 1293.11105 J. Number Theory 132, No. 10, 2336-2352 (2012). MSC: 11T23 14H10 PDF BibTeX XML Cite \textit{R. Blache}, J. Number Theory 132, No. 10, 2336--2352 (2012; Zbl 1293.11105) Full Text: DOI OpenURL
Ivanyos, Gábor; Sanselme, Luc; Santha, Miklos An efficient quantum algorithm for the hidden subgroup problem in nil-2 groups. (English) Zbl 1236.68071 Algorithmica 62, No. 1-2, 480-498 (2012). MSC: 68Q12 20D15 81P68 PDF BibTeX XML Cite \textit{G. Ivanyos} et al., Algorithmica 62, No. 1--2, 480--498 (2012; Zbl 1236.68071) Full Text: DOI arXiv OpenURL
Cao, Wei A partial improvement of the Ax-Katz theorem. (English) Zbl 1282.11161 J. Number Theory 132, No. 4, 485-494 (2012). Reviewer: John H. Loxton (Greenwich, NSW) MSC: 11T06 PDF BibTeX XML Cite \textit{W. Cao}, J. Number Theory 132, No. 4, 485--494 (2012; Zbl 1282.11161) Full Text: DOI OpenURL
Brink, David Chevalley’s theorem with restricted variables. (English) Zbl 1249.11057 Combinatorica 31, No. 1, 127-130 (2011). Reviewer: Hemar Godinho (Brasilia) MSC: 11D79 20K01 11B75 PDF BibTeX XML Cite \textit{D. Brink}, Combinatorica 31, No. 1, 127--130 (2011; Zbl 1249.11057) Full Text: DOI OpenURL
Castro, Francis N.; Randriam, Hugues; Rubio, Ivelisse; Mattson, H. F. jun. Divisibility of exponential sums via elementary methods. (English) Zbl 1203.11082 J. Number Theory 130, No. 7, 1520-1536 (2010). Reviewer: John H. Loxton (Greenwich) MSC: 11T23 11D79 PDF BibTeX XML Cite \textit{F. N. Castro} et al., J. Number Theory 130, No. 7, 1520--1536 (2010; Zbl 1203.11082) Full Text: DOI OpenURL
Chen, Jianming; Cao, Wei Degree matrices and divisibility of exponential sums over finite fields. (English) Zbl 1217.11118 Arch. Math. 94, No. 5, 435-441 (2010). MSC: 11T23 11H06 11D79 PDF BibTeX XML Cite \textit{J. Chen} and \textit{W. Cao}, Arch. Math. 94, No. 5, 435--441 (2010; Zbl 1217.11118) Full Text: DOI OpenURL
Katz, Daniel J. Point count divisibility for algebraic sets over \(\mathbb Z/p^\ell \mathbb Z\) and other finite principal rings. (English) Zbl 1226.11127 Proc. Am. Math. Soc. 137, No. 12, 4065-4075 (2009). MSC: 11T06 13M10 PDF BibTeX XML Cite \textit{D. J. Katz}, Proc. Am. Math. Soc. 137, No. 12, 4065--4075 (2009; Zbl 1226.11127) Full Text: DOI OpenURL
Nikolov, Nikolay; Segal, Dan A characterization of finite soluble groups. (English) Zbl 1122.20007 Bull. Lond. Math. Soc. 39, No. 2, 209-213 (2007). Reviewer: John D. Dixon (Ottawa) MSC: 20D10 20P05 PDF BibTeX XML Cite \textit{N. Nikolov} and \textit{D. Segal}, Bull. Lond. Math. Soc. 39, No. 2, 209--213 (2007; Zbl 1122.20007) Full Text: DOI OpenURL
Illusie, Luc Miscellany on traces in \(\ell\)-adic cohomology: a survey. (English) Zbl 1156.14309 Jpn. J. Math. (3) 1, No. 1, 107-136 (2006). MSC: 14F20 14F10 20G15 PDF BibTeX XML Cite \textit{L. Illusie}, Jpn. J. Math. (3) 1, No. 1, 107--136 (2006; Zbl 1156.14309) Full Text: DOI OpenURL
Hou, Xiang-Dong A note on the proof of a theorem of Katz. (English) Zbl 1144.11082 Finite Fields Appl. 11, No. 2, 316-319 (2005). Reviewer: Olaf Ninnemann (Berlin) MSC: 11T24 11L40 11T30 PDF BibTeX XML Cite \textit{X.-D. Hou}, Finite Fields Appl. 11, No. 2, 316--319 (2005; Zbl 1144.11082) Full Text: DOI OpenURL
Shalev, Aner A partition result for algebraic varieties. (English) Zbl 0731.11035 Proc. Am. Math. Soc. 111, No. 3, 619-624 (1991). Reviewer: Saburô Uchiyama (Tsukuba) MSC: 11G25 12E12 14A10 PDF BibTeX XML Cite \textit{A. Shalev}, Proc. Am. Math. Soc. 111, No. 3, 619--624 (1991; Zbl 0731.11035) Full Text: DOI OpenURL
Wan, Daqing Zeros of diagonal equations over finite fields. (English) Zbl 0659.10017 Proc. Am. Math. Soc. 103, No. 4, 1049-1052 (1988). MSC: 11D99 11D72 11T55 PDF BibTeX XML Cite \textit{D. Wan}, Proc. Am. Math. Soc. 103, No. 4, 1049--1052 (1988; Zbl 0659.10017) Full Text: DOI OpenURL
Mazur, B. Frobenius and the Hodge filtration. (English) Zbl 0258.14006 Bull. Am. Math. Soc. 78, 653-667 (1972). MSC: 14G20 14G15 14G10 14F30 PDF BibTeX XML Cite \textit{B. Mazur}, Bull. Am. Math. Soc. 78, 653--667 (1972; Zbl 0258.14006) Full Text: DOI OpenURL
Terjanian, Guy Dimension arithmétique d’un corps. (French) Zbl 0242.13008 J. Algebra 22, 517-545 (1972). MSC: 13B25 12F05 11D72 PDF BibTeX XML Cite \textit{G. Terjanian}, J. Algebra 22, 517--545 (1972; Zbl 0242.13008) Full Text: DOI OpenURL