Phillips, Tristan Counting Drinfeld modules with prescribed local conditions. (English) Zbl 07818535 Res. Number Theory 10, No. 1, Paper No. 21, 22 p. (2024). MSC: 11G09 11G18 11G50 11D45 14G05 PDFBibTeX XMLCite \textit{T. Phillips}, Res. Number Theory 10, No. 1, Paper No. 21, 22 p. (2024; Zbl 07818535) Full Text: DOI arXiv
Wilsch, Florian Integral points of bounded height on a certain toric variety. (English) Zbl 07814403 Trans. Am. Math. Soc., Ser. B 11, 567-599 (2024). MSC: 11D45 11G35 14G05 PDFBibTeX XMLCite \textit{F. Wilsch}, Trans. Am. Math. Soc., Ser. B 11, 567--599 (2024; Zbl 07814403) Full Text: DOI arXiv
Swaminathan, Ashvin A. Most odd-degree binary forms fail to primitively represent a square. (English) Zbl 07810322 Compos. Math. 160, No. 3, 481-517 (2024). MSC: 11D45 14G05 20G25 14H25 PDFBibTeX XMLCite \textit{A. A. Swaminathan}, Compos. Math. 160, No. 3, 481--517 (2024; Zbl 07810322) Full Text: DOI
Blomer, Valentin; Brüdern, Jörg; Derenthal, Ulrich; Gagliardi, Giuliano The Manin-peyre conjecture for smooth spherical Fano varieties of semisimple rank one. (English) Zbl 07801001 Forum Math. Sigma 12, Paper No. e11, 93 p. (2024). MSC: 14G05 11D45 14M27 11G35 PDFBibTeX XMLCite \textit{V. Blomer} et al., Forum Math. Sigma 12, Paper No. e11, 93 p. (2024; Zbl 07801001) Full Text: DOI arXiv OA License
Chow, Dylon; Loughran, Daniel; Takloo-Bighash, Ramin; Tanimoto, Sho Campana points on wonderful compactifications. arXiv:2403.14433 Preprint, arXiv:2403.14433 [math.NT] (2024). MSC: 14G05 11D45 BibTeX Cite \textit{D. Chow} et al., ``Campana points on wonderful compactifications'', Preprint, arXiv:2403.14433 [math.NT] (2024) Full Text: arXiv OA License
Glas, Jakob; Hochfilzer, Leonhard Rational points on del Pezzo surfaces of low degree. arXiv:2401.04759 Preprint, arXiv:2401.04759 [math.NT] (2024). MSC: 11D45 11G05 11G35 14G05 11H06 BibTeX Cite \textit{J. Glas} and \textit{L. Hochfilzer}, ``Rational points on del Pezzo surfaces of low degree'', Preprint, arXiv:2401.04759 [math.NT] (2024) Full Text: arXiv OA License
Gamburd, Alexander Arithmetic and dynamics on varieties of Markoff type. (English) Zbl 07823043 Beliaev, Dmitry (ed.) et al., International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6–14, 2022. Volume 3. Sections 1–4. Berlin: European Mathematical Society (EMS). 1800-1836 (2023). MSC: 14G12 11N36 11D45 37P55 PDFBibTeX XMLCite \textit{A. Gamburd}, in: International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6--14, 2022. Volume 3. Sections 1--4. Berlin: European Mathematical Society (EMS). 1800--1836 (2023; Zbl 07823043) Full Text: DOI OA License
Heath-Brown, D. R. The distribution of rational points on conics. (English) Zbl 07768660 Acta Arith. 209, 91-128 (2023). MSC: 11D45 11D09 11E08 14G05 PDFBibTeX XMLCite \textit{D. R. Heath-Brown}, Acta Arith. 209, 91--128 (2023; Zbl 07768660) Full Text: DOI arXiv
Lemos, Pedro; Torzewski, Alex Bounds on the number of rational points of curves in families. (English) Zbl 07738035 Bull. Lond. Math. Soc. 55, No. 2, 1019-1032 (2023). MSC: 11D45 11G30 14G05 11D88 PDFBibTeX XMLCite \textit{P. Lemos} and \textit{A. Torzewski}, Bull. Lond. Math. Soc. 55, No. 2, 1019--1032 (2023; Zbl 07738035) Full Text: DOI arXiv OA License
Bonolis, Dante; Browning, Tim Uniform bounds for rational points on hyperelliptic fibrations. (English) Zbl 07697297 Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 24, No. 1, 173-204 (2023); erratum ibid. 24, No. 4, 2501-2504 (2023). MSC: 11D45 14G05 11L40 11N36 PDFBibTeX XMLCite \textit{D. Bonolis} and \textit{T. Browning}, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 24, No. 1, 173--204 (2023; Zbl 07697297) Full Text: DOI arXiv
Browning, Tim; Sawin, Will Free rational curves on low degree hypersurfaces and the circle method. (English) Zbl 1524.14059 Algebra Number Theory 17, No. 3, 719-748 (2023). Reviewer: B. Z. Moroz (Bonn) MSC: 14H10 11D45 11P55 14G05 14J20 PDFBibTeX XMLCite \textit{T. Browning} and \textit{W. Sawin}, Algebra Number Theory 17, No. 3, 719--748 (2023; Zbl 1524.14059) Full Text: DOI arXiv
Ghosh, Aritra; Kumar, Sumit; Mallesham, Kummari; Singh, Saurabh Kumar Bounds for del Pezzo surfaces of degree two. (English) Zbl 07673943 Q. J. Math. 74, No. 1, 247-271 (2023). MSC: 11D45 11N36 14G05 14J26 PDFBibTeX XMLCite \textit{A. Ghosh} et al., Q. J. Math. 74, No. 1, 247--271 (2023; Zbl 07673943) Full Text: DOI arXiv
Browning, Tim; Le Boudec, Pierre; Sawin, Will The Hasse principle for random Fano hypersurfaces. (English) Zbl 07668528 Ann. Math. (2) 197, No. 3, 1115-1203 (2023). Reviewer: David McKinnon (Waterloo) MSC: 11D45 11G50 11P21 14G05 PDFBibTeX XMLCite \textit{T. Browning} et al., Ann. Math. (2) 197, No. 3, 1115--1203 (2023; Zbl 07668528) Full Text: DOI arXiv
Čoupek, Pavel; Lilienfeldt, David T.-B. G.; Xiao, Luciena X.; Yao, Zijian Geometric quadratic Chabauty over number fields. (English) Zbl 1517.11068 Trans. Am. Math. Soc. 376, No. 4, 2573-2613 (2023). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11G30 11D45 14G05 PDFBibTeX XMLCite \textit{P. Čoupek} et al., Trans. Am. Math. Soc. 376, No. 4, 2573--2613 (2023; Zbl 1517.11068) Full Text: DOI arXiv
Santens, Tim Manin’s conjecture for integral points on toric varieties. arXiv:2312.13914 Preprint, arXiv:2312.13914 [math.NT] (2023). MSC: 11D45 11G35 11G50 14G05 BibTeX Cite \textit{T. Santens}, ``Manin's conjecture for integral points on toric varieties'', Preprint, arXiv:2312.13914 [math.NT] (2023) Full Text: arXiv OA License
Matsuzawa, Yohsuke; Suzuki, Yuta Distribution of rational points on random Fano hypersurfaces. arXiv:2310.13408 Preprint, arXiv:2310.13408 [math.NT] (2023). MSC: 11D45 11P21 14G05 BibTeX Cite \textit{Y. Matsuzawa} and \textit{Y. Suzuki}, ``Distribution of rational points on random Fano hypersurfaces'', Preprint, arXiv:2310.13408 [math.NT] (2023) Full Text: arXiv OA License
Yin, John Counting Rational Points on the Stacky \(\operatorname{Sym}^2\mathbb{P}^1\). arXiv:2309.14549 Preprint, arXiv:2309.14549 [math.NT] (2023). MSC: 11D45 11G35 11G40 11G50 14G05 BibTeX Cite \textit{J. Yin}, ``Counting Rational Points on the Stacky $\operatorname{Sym}^2\mathbb{P}^1$'', Preprint, arXiv:2309.14549 [math.NT] (2023) Full Text: arXiv OA License
Ortmann, Judith Integral Points on a del Pezzo Surface over Imaginary Quadratic Fields. arXiv:2307.12877 Preprint, arXiv:2307.12877 [math.NT] (2023). MSC: 11D45 11G35 11R11 14G05 14J26 BibTeX Cite \textit{J. Ortmann}, ``Integral Points on a del Pezzo Surface over Imaginary Quadratic Fields'', Preprint, arXiv:2307.12877 [math.NT] (2023) Full Text: arXiv OA License
Glas, Jakob Complete intersections of cubic and quadric hypersurfaces over \(\mathbb{F}_q(t)\). arXiv:2306.02718 Preprint, arXiv:2306.02718 [math.NT] (2023). MSC: 11D45 11P55 11T55 14G05 BibTeX Cite \textit{J. Glas}, ``Complete intersections of cubic and quadric hypersurfaces over $\mathbb{F}_q(t)$'', Preprint, arXiv:2306.02718 [math.NT] (2023) Full Text: arXiv OA License
Balestrieri, Francesca; Brandes, Julia; Kaesberg, Miriam; Ortmann, Judith; Pieropan, Marta; Winter, Rosa Campana points on diagonal hypersurfaces. arXiv:2302.08164 Preprint, arXiv:2302.08164 [math.NT] (2023). MSC: 11D45 11P55 14G05 BibTeX Cite \textit{F. Balestrieri} et al., ``Campana points on diagonal hypersurfaces'', Preprint, arXiv:2302.08164 [math.NT] (2023) Full Text: arXiv OA License
Binyamini, Gal; Cluckers, Raf; Novikov, Dmitry Bounds for rational points on algebraic curves, optimal in the degree, and dimension growth. arXiv:2302.04209 Preprint, arXiv:2302.04209 [math.NT] (2023). MSC: 11D45 14G05 34C10 11G35 BibTeX Cite \textit{G. Binyamini} et al., ``Bounds for rational points on algebraic curves, optimal in the degree, and dimension growth'', Preprint, arXiv:2302.04209 [math.NT] (2023) Full Text: arXiv OA License
Vermeulen, Floris Points of bounded height on curves and the dimension growth conjecture over \(\mathbb{F}_q[t]\). (English) Zbl 1521.11044 Bull. Lond. Math. Soc. 54, No. 2, 635-654 (2022). MSC: 11G35 11D45 14G05 PDFBibTeX XMLCite \textit{F. Vermeulen}, Bull. Lond. Math. Soc. 54, No. 2, 635--654 (2022; Zbl 1521.11044) Full Text: DOI arXiv
Liu, Chunhui On the global determinant method. (English) Zbl 07714405 Bull. Soc. Math. Fr. 150, No. 4, 699-741 (2022). MSC: 11D45 11G50 14G05 14G25 14G40 PDFBibTeX XMLCite \textit{C. Liu}, Bull. Soc. Math. Fr. 150, No. 4, 699--741 (2022; Zbl 07714405) Full Text: DOI arXiv
Duke, William A Diophantine problem about Kummer surfaces. (English) Zbl 1528.11019 Essent. Number Theory 1, No. 1, 51-56 (2022). Reviewer: Piotr Pokora (Kraków) MSC: 11D45 11E76 14J28 PDFBibTeX XMLCite \textit{W. Duke}, Essent. Number Theory 1, No. 1, 51--56 (2022; Zbl 1528.11019) Full Text: DOI
Zhai, Wenguang Manin’s conjecture for a class of singular cubic hypersurfaces. (English) Zbl 1522.11020 Front. Math. China 17, No. 6, 1089-1132 (2022). MSC: 11D45 11N37 14G05 PDFBibTeX XMLCite \textit{W. Zhai}, Front. Math. China 17, No. 6, 1089--1132 (2022; Zbl 1522.11020) Full Text: DOI
Demirhan, Arda; Takloo-Bighash, Ramin Distribution of rational points on toric varieties: all the heights. (English) Zbl 1520.14049 Res. Math. Sci. 9, No. 4, Paper No. 66, 15 p. (2022). MSC: 14G05 11D45 11G50 11M41 14M25 PDFBibTeX XMLCite \textit{A. Demirhan} and \textit{R. Takloo-Bighash}, Res. Math. Sci. 9, No. 4, Paper No. 66, 15 p. (2022; Zbl 1520.14049) Full Text: DOI arXiv
Paredes, Marcelo; Sasyk, Román Uniform bounds for the number of rational points on varieties over global fields. (English) Zbl 07628585 Algebra Number Theory 16, No. 8, 1941-2000 (2022). Reviewer: Stanley Yao Xiao (Waterloo) MSC: 11D45 11G35 11G50 14G05 PDFBibTeX XMLCite \textit{M. Paredes} and \textit{R. Sasyk}, Algebra Number Theory 16, No. 8, 1941--2000 (2022; Zbl 07628585) Full Text: DOI arXiv
Shute, Alec On the leading constant in the Manin-type conjecture for Campana points. (English) Zbl 1517.11072 Acta Arith. 204, No. 4, 317-346 (2022). MSC: 11G50 11D45 14G05 PDFBibTeX XMLCite \textit{A. Shute}, Acta Arith. 204, No. 4, 317--346 (2022; Zbl 1517.11072) Full Text: DOI arXiv
Streeter, Sam Campana points and powerful values of norm forms. (English) Zbl 1516.11070 Math. Z. 301, No. 1, 627-664 (2022). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11G35 11D45 11D57 11G50 14G05 PDFBibTeX XMLCite \textit{S. Streeter}, Math. Z. 301, No. 1, 627--664 (2022; Zbl 1516.11070) Full Text: DOI arXiv
Takeda, Wataru The distribution of rational points for a class of quartic hypersurfaces. (English) Zbl 1496.11055 Res. Number Theory 8, No. 1, Paper No. 17, 14 p. (2022). Reviewer: Nuno Arala (Coventry) MSC: 11D45 11D25 11N37 14G05 PDFBibTeX XMLCite \textit{W. Takeda}, Res. Number Theory 8, No. 1, Paper No. 17, 14 p. (2022; Zbl 1496.11055) Full Text: DOI
Cao, Yang; Huang, Zhizhong Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics. (English) Zbl 1493.14038 Adv. Math. 398, Article ID 108236, 53 p. (2022). MSC: 14G05 14G12 11D45 11N35 PDFBibTeX XMLCite \textit{Y. Cao} and \textit{Z. Huang}, Adv. Math. 398, Article ID 108236, 53 p. (2022; Zbl 1493.14038) Full Text: DOI arXiv
Heath-Brown, D. R. Equidistribution for Solutions of \(p+m^2+n^2=N\), and for Châtelet Surfaces. arXiv:2212.12587 Preprint, arXiv:2212.12587 [math.NT] (2022). MSC: 11D45 11G35 11G50 11P55 14G05 14G25 BibTeX Cite \textit{D. R. Heath-Brown}, ``Equidistribution for Solutions of $p+m^2+n^2=N$, and for Ch\^{a}telet Surfaces'', Preprint, arXiv:2212.12587 [math.NT] (2022) Full Text: arXiv OA License
Loughran, Daniel; Rome, Nick; Sofos, Efthymios The leading constant for rational points in families. arXiv:2210.13559 Preprint, arXiv:2210.13559 [math.NT] (2022). MSC: 14G05 11E20 11D45 14D10 11N36 BibTeX Cite \textit{D. Loughran} et al., ``The leading constant for rational points in families'', Preprint, arXiv:2210.13559 [math.NT] (2022) Full Text: arXiv OA License
Bodin, Arnaud; Dèbes, Pierre; Najib, Salah WITHDRAWN: Polynomial equations modulo prime numbers. arXiv:2207.06033 Preprint, arXiv:2207.06033 [math.NT] (2022); retraction notice ibid. MSC: 11D45 11T06 11D79 11L20 14G15 BibTeX Cite \textit{A. Bodin} et al., ``WITHDRAWN: Polynomial equations modulo prime numbers'', Preprint, arXiv:2207.06033 [math.NT] (2022); retraction notice ibid. Full Text: arXiv OA License
Schefer, Gerold Counting torsion points on subvarieties of the algebraic torus. arXiv:2209.11441 Preprint, arXiv:2209.11441 [math.NT] (2022). MSC: 11D45 11G25 14G15 BibTeX Cite \textit{G. Schefer}, ``Counting torsion points on subvarieties of the algebraic torus'', Preprint, arXiv:2209.11441 [math.NT] (2022) Full Text: arXiv OA License
Glas, Jakob; Hochfilzer, Leonhard On a question of Davenport and diagonal cubic forms over \(\mathbb{F}_q(t)\). arXiv:2208.05422 Preprint, arXiv:2208.05422 [math.NT] (2022). MSC: 11D45 11P05 11P55 11T55 14G05 BibTeX Cite \textit{J. Glas} and \textit{L. Hochfilzer}, ``On a question of Davenport and diagonal cubic forms over $\mathbb{F}_q(t)$'', Preprint, arXiv:2208.05422 [math.NT] (2022) Full Text: arXiv OA License
Khayutin, Ilya; Nelson, Paul D.; Steiner, Raphael S. Theta functions, fourth moments of eigenforms, and the sup-norm problem II. arXiv:2207.12351 Preprint, arXiv:2207.12351 [math.NT] (2022). MSC: 11F12 11F27 11F70 11F72 11D45 11N75 14G35 BibTeX Cite \textit{I. Khayutin} et al., ``Theta functions, fourth moments of eigenforms, and the sup-norm problem II'', Preprint, arXiv:2207.12351 [math.NT] (2022) Full Text: arXiv OA License
Phillips, Tristan Points of bounded height on projective spaces over global function fields via geometry of numbers. arXiv:2206.07613 Preprint, arXiv:2206.07613 [math.NT] (2022). MSC: 11D45 11G50 11G25 11G45 14G05 BibTeX Cite \textit{T. Phillips}, ``Points of bounded height on projective spaces over global function fields via geometry of numbers'', Preprint, arXiv:2206.07613 [math.NT] (2022) Full Text: arXiv OA License
Phillips, Tristan Points of bounded height on weighted projective spaces over global function fields. arXiv:2205.15877 Preprint, arXiv:2205.15877 [math.NT] (2022). MSC: 11D45 11G50 11M38 11G25 14D23 BibTeX Cite \textit{T. Phillips}, ``Points of bounded height on weighted projective spaces over global function fields'', Preprint, arXiv:2205.15877 [math.NT] (2022) Full Text: arXiv OA License
Phillips, Tristan Average analytic ranks of elliptic curves over number fields. arXiv:2205.09527 Preprint, arXiv:2205.09527 [math.NT] (2022). MSC: 11G05 11D45 11G07 11G35 11G40 11G50 14G05 BibTeX Cite \textit{T. Phillips}, ``Average analytic ranks of elliptic curves over number fields'', Preprint, arXiv:2205.09527 [math.NT] (2022) Full Text: arXiv OA License
Blomer, Valentin; Brüdern, Jörg; Derenthal, Ulrich; Gagliardi, Giuliano The Manin-Peyre conjecture for smooth spherical Fano threefolds. arXiv:2203.14841 Preprint, arXiv:2203.14841 [math.NT] (2022). MSC: 11D45 14M27 14G05 11G35 BibTeX Cite \textit{V. Blomer} et al., ``The Manin-Peyre conjecture for smooth spherical Fano threefolds'', Preprint, arXiv:2203.14841 [math.NT] (2022) Full Text: arXiv OA License
Phillips, Tristan Rational Points of Bounded Height on Some Genus Zero Modular Curves over Number Fields. arXiv:2201.10624 Preprint, arXiv:2201.10624 [math.NT] (2022). MSC: 11G05 11D45 11G07 11G35 11G40 11G50 14G05 BibTeX Cite \textit{T. Phillips}, ``Rational Points of Bounded Height on Some Genus Zero Modular Curves over Number Fields'', Preprint, arXiv:2201.10624 [math.NT] (2022) Full Text: arXiv OA License
Zhang, Runlin Translates of homogeneous measures associated with observable subgroups on some homogeneous spaces. (English) Zbl 1489.37006 Compos. Math. 157, No. 12, 2657-2698 (2021). MSC: 37A17 11D45 11P21 14M17 22E40 22F30 PDFBibTeX XMLCite \textit{R. Zhang}, Compos. Math. 157, No. 12, 2657--2698 (2021; Zbl 1489.37006) Full Text: DOI arXiv
Brandes, Julia; Parsell, Scott T. The Hasse principle for diagonal forms restricted to lower-degree hypersurfaces. (English) Zbl 07463743 Algebra Number Theory 15, No. 9, 2289-2314 (2021). Reviewer: Nuno Arala (Coventry) MSC: 11D72 11D45 11P55 14G05 PDFBibTeX XMLCite \textit{J. Brandes} and \textit{S. T. Parsell}, Algebra Number Theory 15, No. 9, 2289--2314 (2021; Zbl 07463743) Full Text: DOI arXiv
Youmbai, Ahmed El Amine; Uludağ, Muhammed; Behloul, Djilali Elliptic curve involving subfamilies of rank at least 5 over \(\mathbb{Q}(t)\) or \(\mathbb{Q}(t,k)\). (English) Zbl 1491.14052 Hacet. J. Math. Stat. 50, No. 3, 721-731 (2021). Reviewer: Mohammad Sadek (New Cairo) MSC: 14H52 11G05 11D45 PDFBibTeX XMLCite \textit{A. E. A. Youmbai} et al., Hacet. J. Math. Stat. 50, No. 3, 721--731 (2021; Zbl 1491.14052) Full Text: DOI
Vemulapalli, Sameera; Wang, Danielle Uniform bounds for the number of rational points on symmetric squares of curves with low Mordell-Weil rank. (English) Zbl 1482.14027 Acta Arith. 199, No. 4, 331-359 (2021). Reviewer: David McKinnon (Waterloo) MSC: 14G05 11D45 14K20 14T90 PDFBibTeX XMLCite \textit{S. Vemulapalli} and \textit{D. Wang}, Acta Arith. 199, No. 4, 331--359 (2021; Zbl 1482.14027) Full Text: DOI arXiv
Browning, Tim; Yamagishi, Shuntaro Arithmetic of higher-dimensional orbifolds and a mixed Waring problem. (English) Zbl 1508.11041 Math. Z. 299, No. 1-2, 1071-1101 (2021). MSC: 11D45 11P55 14G05 PDFBibTeX XMLCite \textit{T. Browning} and \textit{S. Yamagishi}, Math. Z. 299, No. 1--2, 1071--1101 (2021; Zbl 1508.11041) Full Text: DOI arXiv
Reznick, Bruce Equal sums of two cubes of quadratic forms. (English) Zbl 1476.11071 Int. J. Number Theory 17, No. 3, 761-786 (2021). Reviewer: Ahmet Tekcan (Bursa) MSC: 11E76 14M99 11D41 11D45 PDFBibTeX XMLCite \textit{B. Reznick}, Int. J. Number Theory 17, No. 3, 761--786 (2021; Zbl 1476.11071) Full Text: DOI arXiv
Le Boudec, Pierre Height of rational points on random Fano hypersurfaces. (English) Zbl 1484.11150 Algebra Number Theory 15, No. 3, 657-672 (2021). Reviewer: David McKinnon (Waterloo) MSC: 11G50 14G05 11D45 PDFBibTeX XMLCite \textit{P. Le Boudec}, Algebra Number Theory 15, No. 3, 657--672 (2021; Zbl 1484.11150) Full Text: DOI arXiv
Axenides, Minos; Floratos, Emmanuel; Nicolis, Stam The arithmetic geometry of \(\mathrm{AdS_2}\) and its continuum limit. (English) Zbl 1466.83094 SIGMA, Symmetry Integrability Geom. Methods Appl. 17, Paper 004, 22 p. (2021). MSC: 83E05 83C57 83C45 81T40 81P17 11B39 11D45 14L35 PDFBibTeX XMLCite \textit{M. Axenides} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 17, Paper 004, 22 p. (2021; Zbl 1466.83094) Full Text: DOI arXiv
Peyre, Emmanuel Beyond heights: slopes and distribution of rational points. (English) Zbl 1458.14035 Peyre, Emmanuel (ed.) et al., Arakelov geometry and diophantine applications. Based on lectures given at the summer school, Grenoble, France, June 12–30, 2017. Cham: Springer. Lect. Notes Math. 2276, 215-279 (2021). MSC: 14G40 11D45 11G50 11-01 14-01 PDFBibTeX XMLCite \textit{E. Peyre}, Lect. Notes Math. 2276, 215--279 (2021; Zbl 1458.14035) Full Text: DOI arXiv
Browning, Tim D.; Heath-Brown, Roger The geometric sieve for quadrics. (English) Zbl 1481.11035 Forum Math. 33, No. 1, 147-165 (2021). Reviewer: B. Z. Moroz (Bonn) MSC: 11D45 11G35 11G50 11P55 14G05 14G25 PDFBibTeX XMLCite \textit{T. D. Browning} and \textit{R. Heath-Brown}, Forum Math. 33, No. 1, 147--165 (2021; Zbl 1481.11035) Full Text: DOI arXiv
Iokibe, Gaku Remark on a paper by Izadi and Baghalaghdam about cubes and fifth powers sums. (English) Zbl 1483.11062 Math. J. Okayama Univ. 63, 53-60 (2021). MSC: 11D41 11D45 14H52 PDFBibTeX XMLCite \textit{G. Iokibe}, Math. J. Okayama Univ. 63, 53--60 (2021; Zbl 1483.11062) Full Text: arXiv Link
Derenthal, Ulrich; Wilsch, Florian Integral points on singular del Pezzo surfaces. arXiv:2109.06778 Preprint, arXiv:2109.06778 [math.NT] (2021). MSC: 11D45 11G35 14G05 14J26 BibTeX Cite \textit{U. Derenthal} and \textit{F. Wilsch}, ``Integral points on singular del Pezzo surfaces'', Preprint, arXiv:2109.06778 [math.NT] (2021) Full Text: DOI arXiv OA License
Yuan, Xinyi Arithmetic bigness and a uniform Bogomolov-type result. arXiv:2108.05625 Preprint, arXiv:2108.05625 [math.NT] (2021). MSC: 14G40 11D45 11G50 BibTeX Cite \textit{X. Yuan}, ``Arithmetic bigness and a uniform Bogomolov-type result'', Preprint, arXiv:2108.05625 [math.NT] (2021) Full Text: arXiv OA License
Chim, Kwok Chi; Luca, Florian Perfect squares representing the number of rational points on elliptic curves over finite field extensions. (English) Zbl 1455.11053 Finite Fields Appl. 67, Article ID 101725, 17 p. (2020). MSC: 11D61 11B37 11J25 11D45 14G05 11J87 14H52 PDFBibTeX XMLCite \textit{K. C. Chim} and \textit{F. Luca}, Finite Fields Appl. 67, Article ID 101725, 17 p. (2020; Zbl 1455.11053) Full Text: DOI arXiv
Browning, Tim D.; Sawin, Will Free rational points on smooth hypersurfaces. (English) Zbl 1462.11083 Comment. Math. Helv. 95, No. 4, 635-659 (2020). Reviewer: Juanjo Rué Perna (Barcelona) MSC: 11P55 11D45 14G05 PDFBibTeX XMLCite \textit{T. D. Browning} and \textit{W. Sawin}, Comment. Math. Helv. 95, No. 4, 635--659 (2020; Zbl 1462.11083) Full Text: DOI arXiv
Derenthal, Ulrich; Pieropan, Marta The split torsor method for Manin’s conjecture. (English) Zbl 1481.11036 Trans. Am. Math. Soc. 373, No. 12, 8485-8524 (2020). Reviewer: B. Z. Moroz (Bonn) MSC: 11D45 11G35 14G05 PDFBibTeX XMLCite \textit{U. Derenthal} and \textit{M. Pieropan}, Trans. Am. Math. Soc. 373, No. 12, 8485--8524 (2020; Zbl 1481.11036) Full Text: DOI arXiv
Browning, T. D.; Heath-Brown, D. R. Density of rational points on a quadric bundle in \(\mathbb{P}^3 \times \mathbb{P}^3 \). (English) Zbl 1477.11058 Duke Math. J. 169, No. 16, 3099-3165 (2020). Reviewer: Emiliano Ambrosi (Strasbourg) MSC: 11D45 11G50 11P55 14G05 14G25 PDFBibTeX XMLCite \textit{T. D. Browning} and \textit{D. R. Heath-Brown}, Duke Math. J. 169, No. 16, 3099--3165 (2020; Zbl 1477.11058) Full Text: DOI arXiv Euclid
Mello, Jorge On semigroup orbits of polynomials and multiplicative orders. (English) Zbl 1472.37093 Bull. Aust. Math. Soc. 102, No. 3, 365-373 (2020). MSC: 37P05 37P55 11D45 14G15 PDFBibTeX XMLCite \textit{J. Mello}, Bull. Aust. Math. Soc. 102, No. 3, 365--373 (2020; Zbl 1472.37093) Full Text: DOI arXiv
Bianchi, Francesca Quadratic Chabauty for (bi)elliptic curves and Kim’s conjecture. (English) Zbl 1479.11113 Algebra Number Theory 14, No. 9, 2369-2416 (2020). MSC: 11G50 11Y50 14H52 11D45 PDFBibTeX XMLCite \textit{F. Bianchi}, Algebra Number Theory 14, No. 9, 2369--2416 (2020; Zbl 1479.11113) Full Text: DOI arXiv
Castryck, Wouter; Cluckers, Raf; Dittmann, Philip; Nguyen, Kien Huu The dimension growth conjecture, polynomial in the degree and without logarithmic factors. (English) Zbl 1480.11083 Algebra Number Theory 14, No. 8, 2261-2294 (2020). MSC: 11G35 14G05 11D45 PDFBibTeX XMLCite \textit{W. Castryck} et al., Algebra Number Theory 14, No. 8, 2261--2294 (2020; Zbl 1480.11083) Full Text: DOI arXiv Link
Liu, Jianya; Wu, Jie; Zhao, Yongqiang On a senary quartic form. (English) Zbl 1463.11105 Period. Math. Hung. 80, No. 2, 237-248 (2020). Reviewer: Steven T. Dougherty (Scranton) MSC: 11D45 11D25 11N45 14G05 PDFBibTeX XMLCite \textit{J. Liu} et al., Period. Math. Hung. 80, No. 2, 237--248 (2020; Zbl 1463.11105) Full Text: DOI arXiv HAL
Dan-Cohen, Ishai Mixed Tate motives and the unit equation. II. (English) Zbl 1452.11076 Algebra Number Theory 14, No. 5, 1175-1237 (2020). Reviewer: Fangzhou Jin (Essen) MSC: 11G55 11D45 14F30 14F35 14F42 14G05 PDFBibTeX XMLCite \textit{I. Dan-Cohen}, Algebra Number Theory 14, No. 5, 1175--1237 (2020; Zbl 1452.11076) Full Text: DOI arXiv
Loughran, Daniel; Takloo-Bighash, Ramin; Tanimoto, Sho Zero-loci of Brauer group elements on semi-simple algebraic groups. (English) Zbl 1454.14063 J. Inst. Math. Jussieu 19, No. 5, 1467-1507 (2020). MSC: 14G05 11D45 14F22 11F72 14G12 PDFBibTeX XMLCite \textit{D. Loughran} et al., J. Inst. Math. Jussieu 19, No. 5, 1467--1507 (2020; Zbl 1454.14063) Full Text: DOI arXiv
van Ittersum, Jan-Willem M. Quantitative results on Diophantine equations in many variables. (English) Zbl 1461.11053 Acta Arith. 194, No. 3, 219-240 (2020). MSC: 11D72 11D45 11P55 14G12 PDFBibTeX XMLCite \textit{J.-W. M. van Ittersum}, Acta Arith. 194, No. 3, 219--240 (2020; Zbl 1461.11053) Full Text: DOI arXiv
Tanimoto, Sho On upper bounds of Manin type. (English) Zbl 1454.14064 Algebra Number Theory 14, No. 3, 751-784 (2020). MSC: 14G05 11D45 11G50 14J28 14J45 PDFBibTeX XMLCite \textit{S. Tanimoto}, Algebra Number Theory 14, No. 3, 751--784 (2020; Zbl 1454.14064) Full Text: DOI arXiv
Hu, L. Q. Counting rational points on biprojective hypersurfaces of bidegree \((1,2)\). (English) Zbl 1486.11049 J. Number Theory 214, 312-325 (2020). Reviewer: David McKinnon (Waterloo) MSC: 11D45 11G35 11G50 11P55 14G25 PDFBibTeX XMLCite \textit{L. Q. Hu}, J. Number Theory 214, 312--325 (2020; Zbl 1486.11049) Full Text: DOI
Cluckers, Raf; Pila, Jonathan; Wilkie, Alex Uniform parameterization of subanalytic sets and Diophantine applications. (English) Zbl 1479.03016 Ann. Sci. Éc. Norm. Supér. (4) 53, No. 1, 1-42 (2020). Reviewer: Alexandra Shlapentokh (Greenville) MSC: 03C64 11D45 11G50 11U09 14P15 PDFBibTeX XMLCite \textit{R. Cluckers} et al., Ann. Sci. Éc. Norm. Supér. (4) 53, No. 1, 1--42 (2020; Zbl 1479.03016) Full Text: DOI arXiv
Triantafillou, Nicholas Restriction of Scalars Chabauty and the \(S\)-unit equation. arXiv:2006.10590 Preprint, arXiv:2006.10590 [math.NT] (2020). MSC: 14G05 11D45 11D59 11G20 BibTeX Cite \textit{N. Triantafillou}, ``Restriction of Scalars Chabauty and the $S$-unit equation'', Preprint, arXiv:2006.10590 [math.NT] (2020) Full Text: arXiv OA License
Rydin Myerson, Simon L. Systems of cubic forms in many variables. (English) Zbl 1443.11209 J. Reine Angew. Math. 757, 309-328 (2019). Reviewer: D. R. Heath-Brown (Garsington) MSC: 11P55 11D45 11D72 11D75 11D25 14G05 PDFBibTeX XMLCite \textit{S. L. Rydin Myerson}, J. Reine Angew. Math. 757, 309--328 (2019; Zbl 1443.11209) Full Text: DOI arXiv
Youmbai, Ahmed El Amine; Behloul, Djilali Rational solutions of the Diophantine equations \(f(x)^2\pm f(y)^2=z^2\). (English) Zbl 1449.11062 Period. Math. Hung. 79, No. 2, 255-260 (2019). Reviewer: Florian Luca (Johannesburg) MSC: 11D45 11D41 14H52 PDFBibTeX XMLCite \textit{A. E. A. Youmbai} and \textit{D. Behloul}, Period. Math. Hung. 79, No. 2, 255--260 (2019; Zbl 1449.11062) Full Text: DOI
Marmon, O.; Vishe, P. On the Hasse principle for quartic hypersurfaces. (English) Zbl 1457.11138 Duke Math. J. 168, No. 14, 2727-2799 (2019). Reviewer: D. R. Heath-Brown (Oxford) MSC: 11P55 11D25 11D45 14G05 PDFBibTeX XMLCite \textit{O. Marmon} and \textit{P. Vishe}, Duke Math. J. 168, No. 14, 2727--2799 (2019; Zbl 1457.11138) Full Text: DOI arXiv Euclid Link
Liu, Jianya; Wu, Jie; Zhao, Yongqiang Manin’s conjecture for a class of singular cubic hypersurfaces. (English) Zbl 1451.11021 Int. Math. Res. Not. 2019, No. 7, 2008-2043 (2019). MSC: 11D45 11N37 14G40 14G12 14J70 PDFBibTeX XMLCite \textit{J. Liu} et al., Int. Math. Res. Not. 2019, No. 7, 2008--2043 (2019; Zbl 1451.11021) Full Text: DOI arXiv
Le Boudec, Pierre A statistical view on the conjecture of Lang about the canonical height on elliptic curves. (English) Zbl 1473.11137 Trans. Am. Math. Soc. 372, No. 12, 8347-8361 (2019). MSC: 11G50 11G05 14G05 11D45 PDFBibTeX XMLCite \textit{P. Le Boudec}, Trans. Am. Math. Soc. 372, No. 12, 8347--8361 (2019; Zbl 1473.11137) Full Text: DOI arXiv
Jahnel, Jörg; Schindler, Damaris On the frequency of algebraic Brauer classes on certain log \(K3\)- surfaces. (English) Zbl 1436.14045 Can. Math. Bull. 62, No. 3, 551-563 (2019). Reviewer: D. R. Heath-Brown (Garsington) MSC: 14G12 14J20 11D45 11E12 14G25 14F22 PDFBibTeX XMLCite \textit{J. Jahnel} and \textit{D. Schindler}, Can. Math. Bull. 62, No. 3, 551--563 (2019; Zbl 1436.14045) Full Text: DOI arXiv
Looper, Nicole Dynamical Galois groups of trinomials and Odoni’s conjecture. (English) Zbl 1462.11103 Bull. Lond. Math. Soc. 51, No. 2, 278-292 (2019). MSC: 11R32 37P15 14G05 11D45 PDFBibTeX XMLCite \textit{N. Looper}, Bull. Lond. Math. Soc. 51, No. 2, 278--292 (2019; Zbl 1462.11103) Full Text: DOI arXiv
Frei, Christopher; Loughran, Daniel Rational points and non-anticanonical height functions. (English) Zbl 1506.11042 Proc. Am. Math. Soc. 147, No. 8, 3209-3223 (2019). MSC: 11D45 11G35 14G05 14J26 PDFBibTeX XMLCite \textit{C. Frei} and \textit{D. Loughran}, Proc. Am. Math. Soc. 147, No. 8, 3209--3223 (2019; Zbl 1506.11042) Full Text: DOI arXiv
Buchholz, Ralph H.; Stingley, Robert P. Heron triangles with three rational medians. (English) Zbl 1418.11052 Rocky Mt. J. Math. 49, No. 2, 405-417 (2019). MSC: 11D45 14G05 PDFBibTeX XMLCite \textit{R. H. Buchholz} and \textit{R. P. Stingley}, Rocky Mt. J. Math. 49, No. 2, 405--417 (2019; Zbl 1418.11052) Full Text: DOI Euclid
Browning, T. D.; Hu, L. Q. Counting rational points on biquadratic hypersurfaces. (English) Zbl 1435.11066 Adv. Math. 349, 920-940 (2019). Reviewer: Damaris Schindler (Göttingen) MSC: 11D45 11G35 11G50 11P55 14G25 PDFBibTeX XMLCite \textit{T. D. Browning} and \textit{L. Q. Hu}, Adv. Math. 349, 920--940 (2019; Zbl 1435.11066) Full Text: DOI arXiv
Balakrishnan, Jennifer S.; Dogra, Netan An effective Chabauty-Kim theorem. (English) Zbl 1428.14034 Compos. Math. 155, No. 6, 1057-1075 (2019). Reviewer: David McKinnon (Waterloo) MSC: 14G05 11D45 11F67 11G15 PDFBibTeX XMLCite \textit{J. S. Balakrishnan} and \textit{N. Dogra}, Compos. Math. 155, No. 6, 1057--1075 (2019; Zbl 1428.14034) Full Text: DOI arXiv
Sadek, Mohammad; El-Sissi, Nermine; Shamsi Zargar, Arman; Zamani, Naser Evaluation of Gaussian hypergeometric series using Huff’s models of elliptic curves. (English) Zbl 1473.11135 Ramanujan J. 48, No. 2, 357-368 (2019). MSC: 11G20 33C05 11D45 11T24 14G05 PDFBibTeX XMLCite \textit{M. Sadek} et al., Ramanujan J. 48, No. 2, 357--368 (2019; Zbl 1473.11135) Full Text: DOI arXiv
Destagnol, Kevin [Salberger, Per] Manin’s conjecture for a family of varieties of higher dimension. (La conjecture de Manin pour une famille de variétés en dimension supérieure.) (French. English summary) Zbl 1419.14026 Math. Proc. Camb. Philos. Soc. 166, No. 3, 433-486 (2019). Reviewer: D. R. Heath-Brown (Garsington) MSC: 14G05 11D45 11N37 14M25 PDFBibTeX XMLCite \textit{K. Destagnol}, Math. Proc. Camb. Philos. Soc. 166, No. 3, 433--486 (2019; Zbl 1419.14026) Full Text: DOI arXiv
Swaminathan, Ashvin Most Integral Odd-Degree Binary Forms Fail to Properly Represent a Square. arXiv:1910.12409 Preprint, arXiv:1910.12409 [math.NT] (2019). MSC: 11D45 14G05 20G25 14H25 BibTeX Cite \textit{A. Swaminathan}, ``Most Integral Odd-Degree Binary Forms Fail to Properly Represent a Square'', Preprint, arXiv:1910.12409 [math.NT] (2019) Full Text: arXiv OA License
Mello, Jorge On semigroup orbits of polynomials in subgroups. arXiv:1910.07637 Preprint, arXiv:1910.07637 [math.NT] (2019). MSC: 11D45 14G15 37P55 BibTeX Cite \textit{J. Mello}, ``On semigroup orbits of polynomials in subgroups'', Preprint, arXiv:1910.07637 [math.NT] (2019) Full Text: arXiv OA License
Tran, Manh Hung Uniform bounds for rational points on complete intersections of two quadric surfaces. (English) Zbl 1434.11081 Acta Arith. 186, No. 4, 301-318 (2018). Reviewer: Olaf Ninnemann (Uffing am Staffelsee) MSC: 11D25 11D45 11G05 14G05 PDFBibTeX XMLCite \textit{M. H. Tran}, Acta Arith. 186, No. 4, 301--318 (2018; Zbl 1434.11081) Full Text: DOI arXiv
Loughran, Daniel The number of varieties in a family which contain a rational point. (English) Zbl 1452.14018 J. Eur. Math. Soc. (JEMS) 20, No. 10, 2539-2588 (2018). Reviewer: Stefan Schröer (Düsseldorf) MSC: 14G05 11D45 14F22 14M25 PDFBibTeX XMLCite \textit{D. Loughran}, J. Eur. Math. Soc. (JEMS) 20, No. 10, 2539--2588 (2018; Zbl 1452.14018) Full Text: DOI arXiv
Wen, Hao; Liu, Chunhui Counting multiplicities in a hypersurface over number fields. (English) Zbl 1453.11049 Algebra Colloq. 25, No. 3, 437-458 (2018). Reviewer: Riccardo Pengo (Lyon) MSC: 11D45 11G50 14G05 14J17 14C17 PDFBibTeX XMLCite \textit{H. Wen} and \textit{C. Liu}, Algebra Colloq. 25, No. 3, 437--458 (2018; Zbl 1453.11049) Full Text: DOI arXiv
Derenthal, Ulrich; Gagliardi, Giuliano Manin’s conjecture for certain spherical threefolds. (English) Zbl 1422.11068 Adv. Math. 337, 39-82 (2018). MSC: 11D45 14M27 14G05 11G35 PDFBibTeX XMLCite \textit{U. Derenthal} and \textit{G. Gagliardi}, Adv. Math. 337, 39--82 (2018; Zbl 1422.11068) Full Text: DOI arXiv
Balakrishnan, Jennifer S.; Dan-Cohen, Ishai; Kim, Minhyong; Wewers, Stefan A non-abelian conjecture of Tate-Shafarevich type for hyperbolic curves. (English) Zbl 1460.11038 Math. Ann. 372, No. 1-2, 369-428 (2018). Reviewer: David McKinnon (Waterloo) MSC: 11D45 14H52 11G50 14F35 PDFBibTeX XMLCite \textit{J. S. Balakrishnan} et al., Math. Ann. 372, No. 1--2, 369--428 (2018; Zbl 1460.11038) Full Text: DOI arXiv
Aabrandt, Andreas; Hansen, Vagn Lundsgaard The circle equation over finite fields. (English) Zbl 1446.11118 Quaest. Math. 41, No. 5, 665-674 (2018). MSC: 11G20 11D45 11A07 14G15 PDFBibTeX XMLCite \textit{A. Aabrandt} and \textit{V. L. Hansen}, Quaest. Math. 41, No. 5, 665--674 (2018; Zbl 1446.11118) Full Text: DOI Link
Frei, Christopher; Loughran, Daniel; Sofos, Efthymios Rational points of bounded height on general conic bundle surfaces. (English) Zbl 1460.11039 Proc. Lond. Math. Soc. (3) 117, No. 2, 407-440 (2018). Reviewer: David McKinnon (Waterloo) MSC: 11D45 14G05 11G35 11N37 PDFBibTeX XMLCite \textit{C. Frei} et al., Proc. Lond. Math. Soc. (3) 117, No. 2, 407--440 (2018; Zbl 1460.11039) Full Text: DOI arXiv
Rydin Myerson, Simon L. Quadratic forms and systems of forms in many variables. (English) Zbl 1442.11057 Invent. Math. 213, No. 1, 205-235 (2018). Reviewer: D. R. Heath-Brown (Garsington) MSC: 11D45 11P55 11D72 11D75 11D09 11G35 14G05 PDFBibTeX XMLCite \textit{S. L. Rydin Myerson}, Invent. Math. 213, No. 1, 205--235 (2018; Zbl 1442.11057) Full Text: DOI arXiv
Le Boudec, Pierre Average rank in families of quadratic twists: a geometric point of view. (English) Zbl 1441.11147 Math. Ann. 371, No. 1-2, 695-705 (2018). Reviewer: Noburo Ishii (Kyoto) MSC: 11G05 14G05 11D45 PDFBibTeX XMLCite \textit{P. Le Boudec}, Math. Ann. 371, No. 1--2, 695--705 (2018; Zbl 1441.11147) Full Text: DOI arXiv
Blomer, Valentin; Brüdern, Jörg Counting in hyperbolic spikes: The Diophantine analysis of multihomogeneous diagonal equations. (English) Zbl 1408.11099 J. Reine Angew. Math. 737, 255-300 (2018). Reviewer: Damaris Schindler (Utrecht) MSC: 11P55 14G05 11G35 11D45 PDFBibTeX XMLCite \textit{V. Blomer} and \textit{J. Brüdern}, J. Reine Angew. Math. 737, 255--300 (2018; Zbl 1408.11099) Full Text: DOI arXiv
Blomer, Valentin; Brüdern, Jörg; Salberger, Per The Manin-Peyre formula for a certain biprojective threefold. (English) Zbl 1437.11048 Math. Ann. 370, No. 1-2, 491-553 (2018). Reviewer: Mahadi Ddamulira (Graz) MSC: 11D45 11G35 11M32 14G05 14J30 PDFBibTeX XMLCite \textit{V. Blomer} et al., Math. Ann. 370, No. 1--2, 491--553 (2018; Zbl 1437.11048) Full Text: DOI arXiv
Hansen, Vagn Lundsgaard; Aabrandt, Andreas On quadratic curves over finite fields. arXiv:1802.10486 Preprint, arXiv:1802.10486 [math.NT] (2018). MSC: 11G20 11D45 11D09 11A07 14G15 BibTeX Cite \textit{V. L. Hansen} and \textit{A. Aabrandt}, ``On quadratic curves over finite fields'', Preprint, arXiv:1802.10486 [math.NT] (2018) Full Text: arXiv OA License
Boudec, Pierre Le Height of rational points on congruent number elliptic curves. arXiv:1802.07136 Preprint, arXiv:1802.07136 [math.NT] (2018). MSC: 11D45 11G05 11G50 14G05 BibTeX Cite \textit{P. Le Boudec}, ``Height of rational points on congruent number elliptic curves'', Preprint, arXiv:1802.07136 [math.NT] (2018) Full Text: arXiv OA License
Rastegar, A. Self-similar fractals and arithmetic dynamics. (English) Zbl 1405.37097 Bull. Iran. Math. Soc. 43, No. 7, 2635-2653 (2017). MSC: 37P55 28A80 14G40 11D45 PDFBibTeX XMLCite \textit{A. Rastegar}, Bull. Iran. Math. Soc. 43, No. 7, 2635--2653 (2017; Zbl 1405.37097) Full Text: arXiv Link
Peyre, Emmanuel Freedom and accumulation. (Liberté et accumulation.) (French) Zbl 1434.11084 Doc. Math. 22, 1615-1659 (2017). MSC: 11D45 11G50 14G40 PDFBibTeX XMLCite \textit{E. Peyre}, Doc. Math. 22, 1615--1659 (2017; Zbl 1434.11084) Full Text: DOI arXiv