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Number of items: 50.
2024
Siksek, Samir and Visser, Robin (2024) Curves with few bad primes over cyclotomic Z_l extensions. Algebra & Number Theory . ISSN 1937-0652. (In Press)
2023
Bennett, Michael A. and Siksek, Samir (2023) Differences between perfect powers : the Lebesgue-Nagell equation. Transactions of the American Mathematical Society, 376 (1). pp. 335-370. doi:10.1090/tran/8734 ISSN 0002-9947.
2022
Siksek, Samir (2022) Integral points on punctured abelian varieties. European Journal of Mathematics, 8 . pp. 687-703. doi:10.1007/s40879-022-00570-4 ISSN 2199-675X.
Bennett, Michael A. and Siksek, Samir (2022) Differences between perfect powers : prime power gaps. Algebra & Number Theory, 376 . pp. 335-370. doi:10.1090/tran/8734 ISSN 1937-0652.
Bennett, Michael A., Michaud-Jacobs, Philippe and Siksek, Samir (2022) Q-curves and the Lebesgue-Nagell equation. Journal de ThΓ©orie des Nombres de Bordeaux, 35 (2). pp. 495-510. doi:10.5802/jtnb.1254 ISSN 1246-7405.
Freitas, Nuno, Kraus, Alain and Siksek, Samir (2022) The unit equation over cyclic number fields of prime degree. Algebra & Number Theory, 15 (10). pp. 2647-2653. doi:10.2140/ant.2021.15.2647 ISSN 1937-0652.
Bennett, Michael, Gherga, Adela, Patel, Vandita and Siksek, Samir (2022) Odd values of the Ramanujan tau function. Mathematische Annalen, 382 . pp. 203-238. doi:10.1007/s00208-021-02241-3 ISSN 0025-5831.
2021
Siksek, Samir (2021) Sums of integer cubes. Proceedings of the National Academy of Sciences of the United States of America, 118 (16). e2103697118. doi:10.1073/pnas.2103697118 ISSN 0027-8424.
Freitas, Nuno, Kraus, Alain and Siksek, Samir (2021) Local criteria for the unit equation and the asymptotic Fermat's Last Theorem. Proceedings of the National Academy of Sciences of the United States of America, 118 (12). e2026449118. doi:10.1073/pnas.2026449118 ISSN 0027-8424.
2020
Freitas, Nuno, Kraus, Alain and Siksek, Samir (2020) On asymptotic Fermat over Z_p extensions of Q. Algebra & Number Theory, 14 (9). pp. 2571-2574. doi:10.2140/ant.2020.14.2571 ISSN 1937-0652.
Derickx, Maarten, Najman , Filip and Siksek, Samir (2020) Elliptic curves over totally real cubic fields are modular. Algebra & Number Theory, 14 (7). pp. 1791-1800. doi:10.2140/ant.2020.14.1791 ISSN 1937-0652.
Freitas, Nuno, Kraus, Alain and Siksek, Samir (2020) Class field theory, Diophantine analysis and the asymptotic Fermat's last theorem. Advances in Mathematics, 363 . 106964. doi:10.1016/j.aim.2019.106964 ISSN 0001-8708.
Siksek, Samir and Bennett, Michael A. (2020) A conjecture of ErdΕs, supersingular primes and short character sums. Annals of Mathematics, 191 (2). pp. 355-392. doi:10.4007/annals.2020.191.2.2 ISSN 0003-486X.
2019
Bennett, Michael A., Patel, Vandita and Siksek, Samir (2019) Shifted powers in Lucas-Lehmer sequences. Research in Number Theory, 5 (1). 15. doi:10.1007/s40993-019-0153-2 ISSN 2363-9555.
2018
Ozman, Ekin and Siksek, Samir (2018) Quadratic points on modular curves. Mathematics of Computation, 88 . pp. 2461-2484. doi:10.1090/mcom/3407 ISSN 0025-5718.
Sengun, Mehmet Haluk and Siksek, Samir (2018) On the asymptotic Fermatβs last theorem over number fields. Commentarii Mathematici Helvetici, 93 (2). pp. 359-375. doi:10.4171/CMH/437 ISSN 0010-2571.
2017
Papanikolopoulos, Stefanos and Siksek, Samir (2017) A Mordell-Weil theorem for cubic hypersurfaces of high dimension. Algebra & Number Theory, 11 (8). pp. 1953-1965. doi:10.2140/ant.2017.11.1953 ISSN 1937-0652.
Bennett, Michael A., Patel, Vandita and Siksek, Samir (2017) Perfect powers that are sums of consecutive cubes. Mathematika, 63 (1). pp. 230-249. doi:10.1112/S0025579316000231 ISSN 0025-5793.
2016
Siksek, Samir (2016) Every integer greater than 454 is the sum of at most seven positive cubes. Algebra & Number Theory, 10 (10). pp. 2093-2119. doi:10.2140/ant.2016.10.2093 ISSN 1944-7833.
Bennett, Michael A. and Siksek, Samir (2016) Rational points on ErdΕsβSelfridge superelliptic curves. Compositio Mathematica, 152 (11). pp. 2249-2254. doi:10.1112/S0010437X16007569 ISSN 0010-437X.
Anni, Samuele and Siksek, Samir (2016) Modular elliptic curves over real abelian fields and the generalized Fermat equation $x^{2\ell}+y^{2m}=z^p$. Algebra & Number Theory, 10 (6). pp. 1147-1172. ISSN 1937-0652.
Bennett, Michael A., Patel, Vandita and Siksek, Samir (2016) Superelliptic equations arising from sums of consecutive powers. Acta Arithmetica, 172 . pp. 377-393. doi:10.4064/aa8305-12-2015 ISSN 0065-1036.
Anni, Samuele, Lemos, Pedro and Siksek, Samir (2016) Residual representations of semistable principally polarized abelian varieties. Research in Number Theory, 2 (1). pp. 1-12. doi:10.1007/s40993-015-0032-4 ISSN 2363-9555.
2015
Anni, Samuele and Siksek, Samir (2015) On Serre's uniformity conjecture for semistable elliptic curves over totally real fields. Mathematische Zeitschrift, 281 (1-2). pp. 193-199. doi:10.1007/s00209-015-1478-8 ISSN 0025-5874.
Freitas, Nuno and Siksek, Samir (2015) The asymptotic Fermatβs Last Theorem for five-sixths of real quadratic fields. Compositio Mathematica, 151 (8). pp. 1395-1415. doi:10.1112/S0010437X14007957 ISSN 0010-437X.
Freitas, Nuno, Le Hung, Bao V. and Siksek, Samir (2015) Elliptic curves over real quadratic fields are modular. Inventiones Mathematicae, 201 (1). pp. 159-206. doi:10.1007/s00222-014-0550-z ISSN 0020-9910.
Freitas, Nuno and Siksek, Samir (2015) Fermatβs Last Theorem over some small real quadratic fields. Algebra & Number Theory, 9 (4). pp. 875-895. doi:10.2140/ant.2015.9.875 ISSN 1937-0652.
2014
Siksek, Samir and Stoll, Michael (2014) The generalised Fermat equation x 2 + y 3 = z 15. Archiv der Mathematik, Volume 102 (Number 5). pp. 411-421. doi:10.1007/s00013-014-0639-z ISSN 0003-889X.
Dahmen, Sander R. and Siksek, Samir (2014) Perfect powers expressible as sums of two fifth or seventh powers. Acta Arithmetica, Volume 164 (Number 1). pp. 65-100. doi:10.4064/aa164-1-5 ISSN 0065-1036.
2012
Siksek, Samir (2012) On the number of MordellβWeil generators for cubic surfaces. Journal of Number Theory, Vol.132 (No.11). pp. 2610-2629. doi:10.1016/j.jnt.2012.05.020 ISSN 0022-314X.
Siksek, Samir and Stoll, M. (2012) Partial descent on hyperelliptic curves and the generalized Fermat equation x3+y4+z5=0. Bulletin of the London Mathematical Society , Vol.44 (No.1). pp. 151-166. doi:10.1112/blms/bdr086 ISSN 0024-6093.
2011
Deajim, Abdulaziz and Siksek, Samir (2011) On the Q-linear independence of the sums βn=1βΟk(n)/n! Journal of Number Theory, Volume 131 (Number 4). pp. 745-749. doi:10.1016/j.jnt.2010.11.009 ISSN 0022-314X.
2010
Luca, Florian and Siksek, Samir (2010) On factorials expressible as sums of at most three Fibonacci numbers. Proceedings of the Edinburgh Mathematical Society, Vol.53 (No.3). pp. 747-763. doi:10.1017/S0013091508000874 ISSN 0013-0915 .
Hargreaves, Kathryn and Siksek, Samir (2010) Cycles and fixed points of happy functions. Journal of Combinatorics and Number Theory, Vol.2 (No.3). pp. 217-229. ISSN 1942-5600.
Siksek, Samir and Stoll, M. (Michael) (2010) On a problem of Hajdu and Tengely. In: 9th International Symposium on Algorithmic Number Theory, Inst Natl Rech Informat Automat, Nancy, France, 19-23 Jul 2010. Published in: Lecture Notes in Computer Science, Volume 6197 pp. 316-330. doi:10.1007/978-3-642-14518-6_25 ISSN 0302-9743.
2009
Abu Muriefah, Fadwa S., Luca, Florian, Siksek, Samir and Tengely, Szabolcs (2009) On the diophantine equation x(2) + C=2y(n). International Journal of Number Theory, Vol.5 (No.6). pp. 1117-1128. doi:10.1142/S1793042109002572 ISSN 1793-0421.
Bugeaud, Yann, Reutenauer, Christophe and Siksek, Samir (2009) A Sturmian sequence related to the uniqueness conjecture for Markoff numbers. Theoretical Computer Science, Vol.410 (No.30-32). pp. 2864-2869. doi:10.1016/j.tcs.2009.02.005 ISSN 0304-3975.
Chen, Imin and Siksek, Samir (2009) Perfect powers expressible as sums of two cubes. Journal of Algebra, Vol.322 (No.3 Sp. Iss. SI). pp. 638-656. doi:10.1016/j.jalgebra.2009.03.010 ISSN 0021-8693.
Siksek, Samir (2009) Chabauty for symmetric powers of curves. Algebra & Number Theory, Vol.3 (No.2). pp. 209-236. doi:10.2140/ant.2009.3.209 ISSN 1937-0652.
Siksek, Samir (2009) Diophantine equations after Fermatβs last theorem. Journal de Theorie des Nombres de Bordeaux, Vol.21 (No.2). pp. 423-434. doi:10.5802/jtnb.679 ISSN 1246-7405.
2008
Bright, M. (Martin) and Siksek, Samir (2008) Functions, reciprocity and the obstruction to divisors on curves. Journal of the London Mathematical Society, Vol.77 (Pt.3). pp. 789-807. doi:10.1112/jlms/jdn007 ISSN 0024-6107.
Bugeaud, Yann, Mignotte, Maurice and Siksek, Samir (2008) A multi-frey approach to some multi-parameter families of diophantine equations. Canadian Journal of Mathematics, Vol.60 (No.3). pp. 491-519. doi:DOI:10.4153/CJM-2008-024-9 ISSN 0008-414X.
Bugeaud, Yann, Luca, Florian, Mignotte, Maurice and Siksek, Samir (2008) Almost powers in the Lucas sequence. Journal de Theorie des Nombres de Bordeaux, Vol.20 (No.3). pp. 555-600. doi:10.5802/jtnb.642 ISSN 1246-7405.
Bugeaud, Yann, Luca, Florian, Mignotte, Maurice and Siksek, Samir (2008) Fibonacci numbers at most one away from a perfect power. Elemente der Mathematik, Vol.63 (No.2). pp. 65-75. doi:10.4171/EM/89 ISSN 0013-6018.
Bugeaud, Yann, Mignotte, Maurice, Siksek, Samir, Stoll, M. and Tengely, Szabolcs (2008) Integral points on hyperelliptic curves. Algebra & Number Theory, Vol.2 (No.8). pp. 859-885. doi:DOI: 10.2140/ant.2008.2.859 ISSN 1937-0652.
2007
Bugeaud, Yann, Luca, Florian, Mignotte, Maurice and Siksek, Samir (2007) Perfect powers from products of terms in Lucas sequences. Journal fur die reine und angewandte Mathematik, Vol.611 . pp. 109-129. doi:10.1515/CRELLE.2007.075 ISSN 0075-4102.
2006
Bugeaud, Yann, Mignotte, Maurice and Siksek, Samir (2006) Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers. Annals of Mathematics, Vol.163 (No.3). pp. 969-1018. doi:10.4007/annals.2006.163.969 ISSN 0003-486X.
Cremona, John and Siksek, Samir (2006) Computing a lower bound for the canonical height on elliptic curves over Q. In: 7th International Symposium on Algorithmic Number Theory, Tech Univ Berlin, Berlin, GERMANY, 23-28 Jul 2006. Published in: Lecture Notes in Computer Science, Volume 4076 pp. 275-286. ISBN 3-540-36075-1. ISSN 0302-9743.
2005
Bugeaud, Yann, Luca, Florian, Mignotte, Maurice and Siksek, Samir (2005) ON PERFECT POWERS IN LUCAS SEQUENCES. INTERNATIONAL JOURNAL OF NUMBER THEORY, 1 (3). pp. 309-332. doi:10.1142/S1793042105000236 ISSN 1793-0421.
2001
Siksek, Samir (2001) Sieving for rational points on hyperelliptic curves. Mathematics of Computation, Vol.70 (No.236). pp. 1661-1674. doi:10.1090/S0025-5718-01-01275-3 ISSN 0025-5718.
This list was generated on Thu Mar 28 11:56:01 2024 GMT.