Publicaties
2022
Wetenschappelijke publicaties
Beukers, F., & Delaygue, E. (2022). Some supercongruences of arbitrary length. Indagationes Mathematicae, 33(5), 946-955. https://doi.org/10.1016/j.indag.2022.04.002
Beukers, F., & Forsgård, J. (2022). Γ -evaluations of hypergeometric series. Ramanujan Journal, 58(3), 677-699. https://doi.org/10.1007/s11139-022-00566-4
2021
Wetenschappelijke publicaties
Beukers, F. (2021). A Matrix Version of Dwork’s Congruences. In A. Bostan, & K. Raschel (Eds.), Transcendence in Algebra, Combinatorics, Geometry and Number Theory: TRANS19 – Transient Transcendence in Transylvania, Brașov, Romania, May 13–17, 2019, Revised and Extended Contributions (1 ed., pp. 47-59). (Springer Proceedings in Mathematics and Statistics; Vol. 373). Springer Cham. https://doi.org/10.1007/978-3-030-84304-5_2
Beukers, F., & Vlasenko, M. (2021). Dwork crystals I. International Mathematics Research Notices, 2021(12), 8807-8844. https://doi.org/10.1093/imrn/rnaa119
Beukers, F., & Vlasenko, M. (2021). Dwork crystals II. International Mathematics Research Notices, 2021(6), 4427-4444. [rnaa120]. https://doi.org/10.1093/imrn/rnaa120
2020
Wetenschappelijke publicaties
Chandrasekhar, K., Ehrenborg, R., & Beukers, F. (2020). A Counting Proof for When 2 Is a Quadratic Residue. American Mathematical Monthly, 127(8), 750 - 751. https://doi.org/10.1080/00029890.2020.1790925
2019
Wetenschappelijke publicaties
Beukers, F. (2019). Fields of Definition of Finite Hypergeometric Functions. In 2017 Matrix Anals (Vol. 2, pp. 391-400). Springer Nature. https://doi.org/10.1007/978-3-030-04161-8_26
2018
Wetenschappelijke publicaties
Beukers, F. (2018). Hypergeometric Functions, from Riemann till Present. In L. Ji, & S-T. Yau (Eds.), Uniformization, Riemann-Hilbert correspondence, Calabi-Yau manifolds & Picard-Fuchs equations (pp. 1-19). (Adv. Let. Math (ALM); Vol. 42). International Press.
Beukers, F., Houben, M., & Straub, A. (2018). Gauss congruences for rational functions in several variables. Acta Arithmetica, 184(4), 341-362. https://doi.org/10.4064/aa170614-13-7
2016
Wetenschappelijke publicaties
Beukers, F. (2016). Hoe bewijs je het priemtweelingvermoeden? Nieuw archief voor wiskunde. Serie 5, 5(17), 94-100.
https://dspace.library.uu.nl/bitstream/handle/1874/345608/priemtweelingvermoeden.pdf?sequence=1
https://dspace.library.uu.nl/bitstream/handle/1874/345608/priemtweelingvermoeden.pdf?sequence=1
Beukers, F. (2016). Monodromy of A-hypergeometric functions. Journal fur die Reine und Angewandte Mathematik, 2016(718), 183-206. https://doi.org/10.1515/crelle-2014-0054
2015
Wetenschappelijke publicaties
Cohen, H., Mellit, A., & Beukers, F. (2015). Finite hypergeometric functions. Pure and Applied Mathematics Quarterly, 11(4), 559-589. https://doi.org/10.4310/PAMQ.2015.v11.n4.a2
Beukers, F., & Jouhet, F. (2015). Duality relations for hypergeometric series. Bulletin of London Mathematical Society, 47(2), 343 - 358. https://doi.org/10.1112/blms/bdv009
2014
Wetenschappelijke publicaties
Beukers, F. (2014). Geodesic continued fractions and LLL. Indagationes Mathematicae, 25(4), 632-645. https://doi.org/10.1016/j.indag.2014.04.003
Vakpublicaties
Beukers, F. (2014). Hypergeometric functions, how special are they? Notices of the American Mathematical Society, 61(1), 48-56. https://doi.org/10.1090/noti1065
2013
Wetenschappelijke publicaties
Beukers, F., & Tijdeman, R. (2013). One-sided power sum and cosine inequalities. Indagationes Mathematicae, 24(2), 373-381. https://doi.org/10.1016/j.indag.2012.11.009
2012
Wetenschappelijke publicaties
Beukers, F., Luca, F., & Oort, F. (2012). Power Values of Divisor Sums. The American mathematical monthly., 119(5), 373-380. https://doi.org/10.4169/amer.math.monthly.119.05.373
2011
Wetenschappelijke publicaties
Beukers, F. (2011). Irreducibility of A-hypergeometric systems. Indagationes Mathematicae, 21(1-2), 30-39. https://doi.org/10.1016/j.indag.2010.12.002
https://dspace.library.uu.nl/bitstream/handle/1874/234361/IrreducibilityBeukers.pdf?sequence=1
https://dspace.library.uu.nl/bitstream/handle/1874/234361/IrreducibilityBeukers.pdf?sequence=1
2010
Wetenschappelijke publicaties
Beukers, F., & Stewart, C. L. (2010). Neighboring powers. Journal of Number Theory, 130(3), 660-679. https://doi.org/10.1016/j.jnt.2009.09.006
https://dspace.library.uu.nl/bitstream/handle/1874/196763/beukersNeighboring-powers_2010.pdf?sequence=1
https://dspace.library.uu.nl/bitstream/handle/1874/196763/beukersNeighboring-powers_2010.pdf?sequence=1
Beukers, F., & Stewart, C. L. (2010). Addendum to " Neighboring powers" [J. Number Theory 130 (3) (2010) 660-679]. Journal of Number Theory, 130(7), 1571. https://doi.org/10.1016/j.jnt.2010.03.006
https://dspace.library.uu.nl/bitstream/handle/1874/196772/beukersAddendum-to-Neighboring-powers-.pdf?sequence=1
https://dspace.library.uu.nl/bitstream/handle/1874/196772/beukersAddendum-to-Neighboring-powers-.pdf?sequence=1
Beukers, F. (2010). Algebraic A-hypergeometric functions. Inventiones Mathematicae, 180(3), 589-610. https://doi.org/10.1007/s00222-010-0238-y
https://dspace.library.uu.nl/bitstream/handle/1874/196775/beukersAlgebraic-A-hypergeometric-functions_2010.pdf?sequence=1
https://dspace.library.uu.nl/bitstream/handle/1874/196775/beukersAlgebraic-A-hypergeometric-functions_2010.pdf?sequence=1
Vakpublicaties
Beukers, F. (2010). Diophantische vergelijkingen : een onmogelijke uitdaging. In J. J. O. O. Wiegerinck (Ed.), Vakantiecursus 2010 - Wiskunde: de uitdaging (pp. 3-22). (CWI syllabus; No. 60). CWI.
https://dspace.library.uu.nl/bitstream/handle/1874/196774/vakantiecursus2010.pdf?sequence=2
https://dspace.library.uu.nl/bitstream/handle/1874/196774/vakantiecursus2010.pdf?sequence=2
2008
Wetenschappelijke publicaties
Beukers, F. (2008). Irrationality of p-adic L-values. Acta Mathematica Sinica (English Series), 24(4), 663-686.
Beukers, F. (2008). Explicit calculation of elliptic fibrations of $K3$-surfaces and their Belyi-maps. Number theory and polynomials. London Mathematical Society lecture note series, 352, 33-51.
2007
Wetenschappelijke publicaties
Beukers, F. (2007). Gauss' hypergeometric function. Arithmetic and geometry around hypergeometric functions. Progress in Mathematics, 260, 23-42.
Beukers, F. (2007). Unitary monodromy of Lamé differential operators. Regular and Chaotic Dynamics, 12(6), 630-641. https://doi.org/10.1134/S1560354707060068
Vakpublicaties
van Asselt, R., Beukers, F., Blankespoor, J., Broer, H., Drijvers, P. H. M., Garst, S., van de Giessen, C., Kaenders, R., Kleijne, W., Kollenveld, M., Peletier, M., Siersma, D., van Streun, A., & Zaal, C. G. (2007). Rijk aan betekenis. Visie op vernieuwd wiskundeonderwijs. Commissie Toekomst WiskundeOnderwijs, cTWO.
2006
Wetenschappelijke publicaties
Beukers, F. (2006). A refined version of the Siegel-Shidlovskii theorem. Annals of Mathematics, 163, 369-379.
https://dspace.library.uu.nl/bitstream/handle/1874/26324/beukers_04_refinedversionofthesiegelshidlovskiitheorem_august2004.pdf?sequence=1
https://dspace.library.uu.nl/bitstream/handle/1874/26324/beukers_04_refinedversionofthesiegelshidlovskiitheorem_august2004.pdf?sequence=1
2004
Wetenschappelijke publicaties
Beukers, F., & van der Waall, H. A. (2004). Lame equations with algebraic solutions. Journal of Differential Equations, 197, 1-25.
https://dspace.library.uu.nl/bitstream/handle/1874/26325/beukers_04_lameequationswithalgebraicsolutions.pdf?sequence=1
https://dspace.library.uu.nl/bitstream/handle/1874/26325/beukers_04_lameequationswithalgebraicsolutions.pdf?sequence=1
2002
Wetenschappelijke publicaties
Beukers, F. (2002). On Dwork's accessory parameter problem. Mathematische Zeitschrift, 241, 425-444.
Beukers, F., & Cushman, R. H. (2002). The complex geometry of the spherical pendulum. Contemporary Mathematics, 292, 47-70.
2001
Wetenschappelijke publicaties
Beukers, F., Sanders, J. A., & Wang, J. P. (2001). On integrability of systems of evolution equations. Journal of Differential Equations, 167.
Beukers, F., Sanders, J. A., & Wang, J. P. (2001). On integrability of Systems of Evolution Equations. Journal of Differential Equations, 172, 396-396.
Vakpublicaties
Beukers, F. (2001). Experimentele Getaltheorie. In M. Bakker (Ed.), Vakantiecursus 2001: Experimentele wiskunde (pp. 3-16). (CWI Syllabus; No. 49). Centrum voor Wiskunde en Informatica.
2000
Wetenschappelijke publicaties
Beukers, F. (2000). The maximal differential ideal is generated by its invariants. Indigationes Mathematicae, 11(1), 13-18.
Vakpublicaties
Beukers, F. (2000). A rational approach to Pi. Nieuw archief voor wiskunde. Serie 5, 1(4), 372-379.
https://dspace.library.uu.nl/bitstream/handle/1874/26398/beukers_00_rationalapproachto_pi.pdf?sequence=1
https://dspace.library.uu.nl/bitstream/handle/1874/26398/beukers_00_rationalapproachto_pi.pdf?sequence=1
Beukers, F. (2000). Pi, de geschiedenis en wiskunde van het getal Pi. (Zebrareeks ed.) Epsilon Uitgaven.
1999
Wetenschappelijke publicaties
Beukers, F. (1999). Integral points on cubic surfaces. Lecture Notes, Centre de Recherches, 19, 25-33.
Beukers, F. (1999). Factorisation of polynomials. In Some tapas of computer algebra (pp. 78-90). (Algorithms Comput. Math.; No. 4). Springer.
Beukers, F., Shorey, T. N., & Tijdeman, R. (1999). Irreducibility of polynomials and arithmetic progressions with equal products of terms. In K. Györy, H. Iwaniec, & J. Urbanowicz (Eds.), Number Theory in Progress, Proceedings Zakopone, Poland 1997 (pp. 11-26). Walter de Gruyter.
Beukers, F. (1999). Lattice reduction. In Some tapas of computer algebra (pp. 66-77). (Algorithms Comput. Math.; No. 4). Springer.
Vakpublicaties
Beukers, F. (1999). P = NP? In M. Bakker (Ed.), Vakantiecursus 1999: Onbewezen vermoedens (pp. 93-108). (CWI syllabus; No. 45). Stichting Mathematisch Centrum.
https://dspace.library.uu.nl/bitstream/handle/1874/26399/beukers_99_p_is_np.pdf?sequence=1
https://dspace.library.uu.nl/bitstream/handle/1874/26399/beukers_99_p_is_np.pdf?sequence=1
Beukers, F. (1999). Getaltheorie voor beginners. Epsilon Uitgaven.
1998
Wetenschappelijke publicaties
Beukers, F., & Cushman, R. H. (1998). Zeeman's monotonicity conjecture. Journal of Differential Equations, 143(1998), 191-200.
Beukers, F., Sanders, J., & Wang, J. P. (1998). One symmetry does not imply integrability. Journal of Differential Equations, 146(1998), 251-260.
Beukers, F. (1998). The diophantine equation. Ax p + By q = CZ r. Duke Mathematical Journal, 91(1998), 61-88.
1997
Wetenschappelijke publicaties
Beukers, F. (1997). On a sequence of polynomials. Journal of Pure and Applied Algebra, 117 & 118, 97-103.
Beukers, F., & Zagier, D. (1997). Lower bounds of heights of points on hypersurfaces. Acta Arithmetica, 79(2), 103-111.
https://dspace.library.uu.nl/bitstream/handle/1874/26374/beukers_07_lowerbounds.pdf?sequence=1
https://dspace.library.uu.nl/bitstream/handle/1874/26374/beukers_07_lowerbounds.pdf?sequence=1
1996
Wetenschappelijke publicaties
Beukers, F., & Schlickewei, H. P. (1996). The equation x+y=1 in finitely generated groups. Acta Arithmetica, 78, 189-199.
https://dspace.library.uu.nl/bitstream/handle/1874/26372/beukers_07_equation_xplusy.pdf?sequence=1
https://dspace.library.uu.nl/bitstream/handle/1874/26372/beukers_07_equation_xplusy.pdf?sequence=1
1995
Wetenschappelijke publicaties
Beukers, F. (1995). Ternary Form Equations. Journal of Number Theory, 54(1), 113-133. https://doi.org/10.1006/jnth.1995.1105
1993
Wetenschappelijke publicaties
Beukers, F. (1993). Algebraic values of G-functions. Journal fur die Reine und Angewandte Mathematik, 1993(434), 45-66. https://doi.org/10.1515/crll.1993.434.45
1991
Wetenschappelijke publicaties
Beukers, F., van der Poorten, A. J., & Yager, R. I. (1991). Dyson's lemma without tears. Indagationes Mathematicae, 2(1), 19-28. https://doi.org/10.1016/0019-3577(91)90038-9
1989
Wetenschappelijke publicaties
Beukers, F., & Heckman, G. (1989). Monodromy for the hypergeometric functionnFn-1. Inventiones Mathematicae, 95(2), 325-354. https://doi.org/10.1007/BF01393900
1987
Wetenschappelijke publicaties
Beukers, F. (1987). Another congruence for the Apéry numbers. Journal of Number Theory, 25(2), 201-210. https://doi.org/10.1016/0022-314X(87)90025-4
1985
Wetenschappelijke publicaties
Stienstra, J., & Beukers, F. (1985). On the Picard-Fuchs equation and the formal brauer group of certain elliptic K3-surfaces. Mathematische Annalen, 271(2), 269-304. https://doi.org/10.1007/BF01455990
Beukers, F. (1985). Some congruences for the Apery numbers. Journal of Number Theory, 21(2), 141-155. https://doi.org/10.1016/0022-314X(85)90047-2
1984
Wetenschappelijke publicaties
Beukers, F., & Peters, C. A. M. (1984). A Family of K 3 Surfaces and ζ(3). Journal fur die Reine und Angewandte Mathematik, 1984(351), 42-54. https://doi.org/10.1515/crll.1984.351.42
Beukers, F., & Huijsmans, C. B. (1984). Calculus in F-Algebras. Journal of the Australian Mathematical Society, 37(1), 110-116. https://doi.org/10.1017/S1446788700021790
1983
Wetenschappelijke publicaties
Beukers, F., Huijsmans, C. B., & de Pagter, B. (1983). Unital embedding and complexification of F-algebras. Mathematische Zeitschrift, 183(1), 131-144. https://doi.org/10.1007/BF01187219
1981
Wetenschappelijke publicaties
Beukers, F. (1981). Fractional parts of powers of rationals. Mathematical Proceedings of the Cambridge Philosophical Society, 90(1), 13-20. https://doi.org/10.1017/S0305004100058485
1980
Wetenschappelijke publicaties
Beukers, F. (1980). Legendre polynomials in irrationality proofs. Bulletin of the Australian Mathematical Society, 22(3), 431-438. https://doi.org/10.1017/S0004972700006742
1979
Wetenschappelijke publicaties
Beukers, F. (1979). A note on the irrationality of ζ (2) and ζ (3. Bulletin of the London Mathematical Society, 11(3), 268-272. https://doi.org/10.1112/blms/11.3.268
1975
Wetenschappelijke publicaties
Beukers, F. (1975). The lattice-points of n-dimensional tetrahedra. Indagationes Mathematicae, 37(5), 365-372.