S. Siksek

发表

Descent on Picard groups using functions on curves

Samir Siksek, S. Siksek, 2002, Bulletin of the Australian Mathematical Society.

Integral points on hyperelliptic curves

M. Mignotte, Y. Bugeaud, M. Stoll, 2008, 0801.4459.

The asymptotic Fermat’s Last Theorem for five-sixths of real quadratic fields

S. Siksek, Nuno Freitas, 2013, Compositio Mathematica.

Sums of integer cubes

S. Siksek, 2021, Proceedings of the National Academy of Sciences.

Class field theory, Diophantine analysis and the asymptotic Fermat's Last Theorem

S. Siksek, Alain Kraus, Nuno Freitas, 2019, Advances in Mathematics.

Almost powers in the Lucas sequence

M. Mignotte, F. Luca, Y. Bugeaud, 2008 .

A Sturmian sequence related to the uniqueness conjecture for Markoff numbers

Yann Bugeaud, Christophe Reutenauer, Samir Siksek, 2009, Theor. Comput. Sci..

Differences between perfect powers : the Lebesgue-Nagell Equation

M. Bennett, S. Siksek, 2021, 2109.09128.

The unit equation over cyclic number fields of prime degree

S. Siksek, Alain Kraus, Nuno Freitas, 2020, Algebra & Number Theory.

Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers

M. Mignotte, Y. Bugeaud, S. Siksek, 2004, math/0403046.

On the complexity of computing the 2-Selmer group of an elliptic curve

N. Smart, S. Siksek, 1997, Glasgow Mathematical Journal.

Explicit 4-descents on an elliptic curve

Samir Siksek, Nigel P. Smart, N. Smart, 1996 .

The generalised Fermat equation x2 + y3 = z15

M. Stoll, S. Siksek, 2013, 1309.4421.

On a Shimura Curve That is a Counterexample to the Hasse Principle

A. Skorobogatov, S. Siksek, 2003 .

Elliptic curves over real quadratic fields are modular

S. Siksek, Nuno Freitas, Bao V. Le Hung, 2014, Inventiones mathematicae.

Odd values of the Ramanujan tau function

Adela Gherga, M. Bennett, S. Siksek, 2021, Mathematische Annalen.

The Generalized Fermat Equation

Samir Siksek, Preda Mihăilescu, Michael A. Bennett, 2016, Open Problems in Mathematics.

On the number of Mordell-Weil generators for cubic surfaces

S. Siksek, 2010, 1012.1838.

Every integer greater than 454 is the sum of at most seven positive cubes

S. Siksek, 2015, 1505.00647.

The Brauer-Manin obstruction for curves having split jacobians

S. Siksek, 2004 .

Classical and modular approaches to exponential Diophantine equations II. The Lebesgue–Nagell equation

Maurice Mignotte, Yann Bugeaud, Samir Siksek, 2004, Compositio Mathematica.

On a Problem of Hajdu and Tengely

Michael Stoll, Samir Siksek, M. Stoll, 2009, ANTS.

Chabauty for symmetric powers of curves

S. Siksek, 2009 .

On Fibonacci numbers with few prime divisors

M. Mignotte, F. Luca, Y. Bugeaud, 2005 .

On standardized models of isogenous elliptic curves

Samir Siksek, S. Siksek, 2004, Math. Comput..

On the Diophantine equation $x^2 + 7 = y^m$

J. Cremona, S. Siksek, 2003 .

Descents on curves of Genus 1

S. Siksek, 1995 .

Primitive algebraic points on curves

S. Siksek, Maleeha Khawaja, 2023, 2306.17772.

Elliptic curves over real quadratic fields are modular

S. Siksek, Nuno Freitas, Bao V. Le Hung, 2013, 1310.7088.

On the asymptotic Fermat’s last theorem over number fields

S. Siksek, Mehmet Haluk Sengun, 2016, Commentarii Mathematici Helvetici.

Elliptic curves over totally real cubic fields are modular

Filip Najman, S. Siksek, M. Derickx, 2019, 1901.03436.

Fermat's Last Theorem over some small real quadratic fields

S. Siksek, Nuno Freitas, 2014, 1407.4435.

Torsion points on elliptic curves over number fields of small degree

G. Rector, B. D. Smit, S. Siksek, 2016 .

Shifted powers in Lucas–Lehmer sequences

M. Bennett, S. Siksek, Vandita Patel, 2018, Research in Number Theory.

Modular elliptic curves over real abelian fields and the generalized Fermat equation $x^{2\ell}+y^{2m}=z^p$

S. Siksek, Samuele Anni, 2015, 1506.02860.

Criteria for irreducibility of mod p representations of Frey curves

S. Siksek, Nuno Freitas, 2013, 1309.4748.

On the Asymptotic Fermat's Last Theorem.

S. Siksek, Nuno Freitas, 2018, 1804.02849.

Differences between perfect powers : prime power gaps

Michael A. Bennett, S. Siksek, M. Bennett, 2021, 2110.05553.

On the diophantine equation

S. Siksek, 2017 .

On factorials expressible as sums of at most three Fibonacci numbers

F. Luca, S. Siksek, 2010, Proceedings of the Edinburgh Mathematical Society.

Fibonacci numbers at most one away from a perfect power

Maurice Mignotte, Yann Bugeaud, Samir Siksek, 2008 .

Perfect powers from products of terms in Lucas sequences

M. Mignotte, F. Luca, Y. Bugeaud, 2007 .

Efficient resolution of Thue-Mahler equations

Adela Gherga, S. Siksek, 2022, 2207.14492.

The Modular Approach to Diophantine Equations

S. Siksek, 2007 .

On the Diophantine Equation X 2 + C = 2y

S. Siksek, Szabolcs Tengely, F. Luca, 2022 .

Shifted powers in Lucas–Lehmer sequences

S. Siksek, Vandita Patel, Michael A. Bennett, 2019, Research in Number Theory.

ON PERFECT POWERS IN LUCAS SEQUENCES

M. Mignotte, F. Luca, Y. Bugeaud, 2005 .

ON THE DIOPHANTINE EQUATION x2 + C = 2yn

F. Luca, S. Siksek, Szabolcs Tengely, 2009 .

des Nombres de Bordeaux 00 ( XXXX ) , 000 – 000 Almost Powers in the Lucas Sequence par

M. Mignotte, F. Luca, Y. Bugeaud, 2008 .

Odd values of the Ramanujan tau function

Samir Siksek, Vandita Patel, Adela Gherga, 2021, Mathematische Annalen.

$\mathbb{Q}$-curves and the Lebesgue-Nagell equation

M. Bennett, S. Siksek, Philippe Michaud-Jacobs, 2022, 2202.09219.

A Multi-Frey Approach to Some Multi-Parameter Families of Diophantine Equations

M. Mignotte, Y. Bugeaud, S. Siksek, 2008, Canadian Journal of Mathematics.

Shifted powers in binary recurrence sequences

M. Mignotte, M. Bennett, S. Siksek, 2014, Mathematical Proceedings of the Cambridge Philosophical Society.

On powers that are sums of consecutive like powers

S. Siksek, Vandita Patel, 2016, Research in number theory.

Superelliptic equations arising from sums of consecutive powers

M. Bennett, S. Siksek, Vandita Patel, 2015, 1509.06619.

Perfect powers that are sums of consecutive cubes

M. Bennett, S. Siksek, Vandita Patel, 2016, 1603.08901.

On the diophantine equation x(2) + C=2y(n)

F. Luca, S. Siksek, Szabolcs Tengely, 2009 .

Chabauty and the Mordell-Weil Sieve

Samir Siksek, S. Siksek, 2015, Advances on Superelliptic Curves and their Applications.

A conjecture of Erdős, supersingular primes and short character sums

M. Bennett, S. Siksek, 2017, Annals of Mathematics.

On Serre’s uniformity conjecture for semistable elliptic curves over totally real fields

S. Siksek, Samuele Anni, 2014, 1408.1279.

Infinite Descent on Elliptic Curves

S. Siksek, 1995 .

Functions, reciprocity and the obstruction to divisors on curves

S. Siksek, M. Bright, 2008 .

On powers that are sums of consecutive like powers

S. Siksek, Vandita Patel, 2016, Research in Number Theory.

Height difference bounds for elliptic curves over number fields

J. Cremona, S. Siksek, M. Prickett, 2006 .

Explicit Arithmetic of Modular Curves

S. Siksek, 2019 .

Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers, submitted

M. Mignotte, S. Siksek, Yann Bugeaud, 2022 .

Perfect powers expressible as sums of two fifth or seventh powers

S. Siksek, S. Dahmen, 2013, 1309.4030.

Partial descent on hyperelliptic curves and the generalized Fermat equation x3+y4+z5=0

M. Stoll, S. Siksek, 2011, 1103.1979.

Explicit Chabauty over number fields

S. Siksek, 2010, 1010.2603.

CYCLES AND FIXED POINTS OF HAPPY FUNCTIONS

S. Siksek, Kathryn Hargreaves, 2010 .

Diophantine equations after Fermat’s last theorem

S. Siksek, 2009 .

Squares in arithmetic progression over cubic fields

S. Siksek, A. Bremner, 2015, 1505.06424.

Computing a Lower Bound for the Canonical Height on Elliptic Curves over Q

Samir Siksek, John Cremona, J. Cremona, 2006, ANTS.