Pastén, Héctor Elliptic surfaces and Hilbert’s tenth problem. (Spanish. English summary) Zbl 07797283 Rev. Mat. Teor. Apl. 30, No. 1, 113-120 (2023). MSC: 11U05 14J27 11G05 PDFBibTeX XMLCite \textit{H. Pastén}, Rev. Mat. Teor. Apl. 30, No. 1, 113--120 (2023; Zbl 07797283) Full Text: DOI
Pasten, Hector Notes on the DPRM property for listable structures. (English) Zbl 1500.11093 J. Symb. Log. 87, No. 1, 273-312 (2022). Reviewer: Alexandra Shlapentokh (Greenville) MSC: 11U09 03D45 11G35 11J68 PDFBibTeX XMLCite \textit{H. Pasten}, J. Symb. Log. 87, No. 1, 273--312 (2022; Zbl 1500.11093) Full Text: DOI arXiv
Garcia-Fritz, Natalia; Pasten, Hector Towards Hilbert’s tenth problem for rings of integers through Iwasawa theory and Heegner points. (English) Zbl 1469.11168 Math. Ann. 377, No. 3-4, 989-1013 (2020). Reviewer: Alexandra Shlapentokh (Greenville) MSC: 11G05 11U05 PDFBibTeX XMLCite \textit{N. Garcia-Fritz} and \textit{H. Pasten}, Math. Ann. 377, No. 3--4, 989--1013 (2020; Zbl 1469.11168) Full Text: DOI arXiv
Murty, M. Ram; Pasten, Hector Elliptic curves, \(L\)-functions, and Hilbert’s tenth problem. (English) Zbl 1441.11300 J. Number Theory 182, 1-18 (2018). Reviewer: Alexandra Shlapentokh (Greenville) MSC: 11U05 11G05 14G10 PDFBibTeX XMLCite \textit{M. R. Murty} and \textit{H. Pasten}, J. Number Theory 182, 1--18 (2018; Zbl 1441.11300) Full Text: DOI
Garcia-Fritz, Natalia; Pasten, Hector Uniform positive existential interpretation of the integers in rings of entire functions of positive characteristic. (English) Zbl 1329.11129 J. Number Theory 156, 368-393 (2015). Reviewer: Alexandra Shlapentokh (Greenville) MSC: 11U05 30G06 12L05 PDFBibTeX XMLCite \textit{N. Garcia-Fritz} and \textit{H. Pasten}, J. Number Theory 156, 368--393 (2015; Zbl 1329.11129) Full Text: DOI arXiv
Pasten, Hector; Pheidas, Thanases; Vidaux, Xavier Uniform existential interpretation of arithmetic in rings of functions of positive characteristic. (English) Zbl 1327.03009 Invent. Math. 196, No. 2, 453-484 (2014). Reviewer: Mihai Prunescu (Bucharest) MSC: 03B25 11U05 12L05 PDFBibTeX XMLCite \textit{H. Pasten} et al., Invent. Math. 196, No. 2, 453--484 (2014; Zbl 1327.03009) Full Text: DOI arXiv
Pasten, Hector Powerful values of polynomials and a conjecture of Vojta. (English) Zbl 1364.11090 J. Number Theory 133, No. 9, 2964-2998 (2013). MSC: 11D85 11J97 11R58 11U05 PDFBibTeX XMLCite \textit{H. Pasten}, J. Number Theory 133, No. 9, 2964--2998 (2013; Zbl 1364.11090) Full Text: DOI
Pasten, Hector Representation of squares by monic second degree polynomials in the field of \(p\)-adic meromorphic functions. (English) Zbl 1252.11093 Trans. Am. Math. Soc. 364, No. 1, 417-446 (2012). Reviewer: Mihai Prunescu (Freiburg i. Br.) MSC: 11U05 30D35 30D30 30G06 PDFBibTeX XMLCite \textit{H. Pasten}, Trans. Am. Math. Soc. 364, No. 1, 417--446 (2012; Zbl 1252.11093) Full Text: DOI arXiv
Pasten, H.; Pheidas, T.; Vidaux, X. A survey on Büchi’s problem: new presentations and open problems. (English) Zbl 1282.11015 J. Math. Sci., New York 171, No. 6, 765-781 (2010) and Zap. Nauchn. Semin. POMI 377, 111-140 (2010). MSC: 11D09 11U05 PDFBibTeX XMLCite \textit{H. Pasten} et al., J. Math. Sci., New York 171, No. 6, 765--781 (2010; Zbl 1282.11015) Full Text: DOI