Local arithmetic of curves and jacobians rachel newton. Pinter, a book of abstract algebra, 2nd edition, dover 2010. Much more sophisticated and concise than the rst two references, and covers lots of advanced topics that we. To see an extisive list of abstract algebra ebooks. Pgl 2 acts on the latter by linear change of variables, twisted by inverse determinant. Computational aspects of the birch and swinnertondyer conjecture adam morgan. Silverman, advanced topics in the arithmetic of elliptic curves. In this paper, we focus on step 1, and we show that step 1 can run in quantum polynomial time if we use an algorithm for the continuous hidden subgroup problem hsp due to eisentrager et al. Teaching assistant, topics in number theory, university of warwick, fall 2011. If you nd yourself really into the subject you might want to dip into the chapter on elds of low degree.
Thanks go to jenny cooley, samantha pilgram and vandita ditz patel for corrections. Their combined citations are counted only for the first article. Topics in number theory, university of warwick, fall 20. The modularity theorem for elliptic curves associated to any. Samir siksek, mathematics institute, university of warwick, coventry, cv4 7al. Topics in computational number theory inspired by peter l. Local class field theory describes the abelian galois extensions of a local field, e. Simon michael stoll explicit ndescent on elliptic curves, i. Siksek samir siksek, introduction to abstract algebra, 2015. Topics in number theory lecture notes, hw 1, hw 2, hw 3, hw 4, hw 5, hw 6. Stage seminar on topics in arithmetic, geometry, etc. Warwick impact award under professor samir siksek, research area. Ranks of elliptic curves in families of quadratic twists rubin, karl and silverberg, alice, experimental mathematics, 2000. Supervisor of undergraduate rst and second year mathematics students, university of warwick, 20082012.
Peter swinnertondyer, a brief guide to algebraic number theory. Fermats last theorem over some small real quadratic fields. The modularity theorem is a special case of more general conjectures due to robert langlands. Thanks go to jenny cooley, samantha pilgram and vandita patel for corrections. The modular approach to diophantine equations, in explicit methods in number theory. Samir siksek professor at the mathematics institute, university of warwick. The asymptotic fermats last theorem for fivesixths of.
In these projects, students either followed up on topics that interested them from the semester, or chose and investigated topics related to number theory. These are my lecture notes for ma3h1 topics in number the ory, with the usual siksek trademarks. Advanced topics in computional number theory request pdf. Research project topics for 20162017 university of warwick. Samir siksek, chabauty for symmetric powers of curves, algebra number theory 3 2009, no. If you have additional information or corrections regarding this mathematician, please use the update form. Samir siksek personal homepage university of warwick. The range of topics included modular forms, varieties over. Ma3h1 topics in number theory samir siksek university of warwick. Topics in number theory lecture notes, hw 1, hw 2, hw 3.
This he proves using classical algebraic number theory, and a. Ma5 vectors and matrices lecture notes samir siksek. Samir siksek warwick galois representations of elliptic curves and diophantine applications. Bosma, proceedings of antsiv, lncs 1838, springer 2000 aliquot sequences wieb bosma. Please read our short guide how to send a book to kindle. Explicit methods in number theory organised by henri cohen, talence hendrik w.
This is an other great mathematics book cover the following topics of problem solving. Introduction by the organisers the workshop explicit methods in number theory was organised. On serres uniformity conjecture for semistable elliptic curves over totally real fields. By yann bugeaud, maurice mignotte and samir siksek. Advanced topics in the arithmetic of elliptic curves, volume. According to our current online database, samir siksek has 14 students and 16 descendants. Pdf explicit arithmetic of modular curves semantic scholar. These notes contain extended abstracts on the topic of explicit methods in number theory. As pgl 2z acts on q dz, one sees that, if v q,dz q. The fundamental theorem of arithmetic every pos itive integer n can be written as a product of prime numbers, this fac torisation into primes is unique up to the. Several theorems in number theory similar to fermats last theorem follow from the modularity theorem. Whether youve loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.
Other readers will always be interested in your opinion of the books youve read. Rational points and diophantine equations, belabas, lenstra. An introduction to elementary number theory at brown university. Algebraic reorientation, matrices, groups, first theorems, orders and lagranges theorem, subgroups, cyclic groups and cyclic subgroups, isomorphisms, cosets, quotient groups, symmetric groups, rings and fields. The queen of mathematics gauss wrote that \mathematics is the queen of sciences and number. The central theme of this graduatelevel number theory textbook is the solution of diophantine equations, i.
Topics in number theory lecture notes, hw 1, hw 2, hw 3, hw 4. Silverman, advanced topics in the arithmetic of elliptic curves, gtm 151, springer. Algebraic reorientation, matrices, groups, first theorems, orders and lagranges theorem, subgroups, cyclic groups and cyclic subgroups, isomorphisms, cosets, quotient groups, symmetric groups, rings. Lenstra, cup 2017 on the cryptanalysis of publickey cryptography, phd thesis, joppe willem bos, epl lausanne, 2012 wieb bosma. Vectors and matrices lecture notes, hw 1, hw 2, hw 3, hw 4, hw 5. The modular approach to diophantine equations mathematical.
Modular elliptic curves over real abelian fields and the generalized. Minimisation and reduction of 2, 3 and 4coverings of elliptic curves. Soma purkait curriculum vitae tokyo institute of technology 2121 ookayama, meguroku. We hope mathematician or person whos interested in mathematics like these books. Henri cohen, a course in computational algebraic number theory, graduate texts in mathematics, vol. Elliptic curves over real quadratic fields are modular. By yann bugeaud, maurice mignotte and samir siksek abstract this is the first in a series of papers whereby we combine the classical approach to exponential diophantine equations linear forms in logarithms, thue equations, etc. To submit students of this mathematician, please use the new data form, noting this mathematicians mgp id of 46521 for the advisor id. On arithmetic progressions on elliptic curves bremner, andrew, experimental mathematics, 1999. Introduction to abstract algebra written by samir siksek.
These are my lecture notes for ma3h1 topics in number theory, with the usual siksek trademarks. If algeraic number theory was a 4th year module this would probably be the right textbook. Please send comments, misprints and corrections to samir. Samir siksek published 2019 these are my notes for a course i gave at the institut henri poincare 29 april3 may 2019 and at cmihimr summer school in computational number theory, bristol 1721 june 2019. John cremona and samir siksek, computing a lower bound for the canonical height on elliptic curves over. This is probably the most amusing though occasionally overdoing the goo. The asymptotic fermats last theorem for fivesixths of real. Introduction by the organisers the workshop explicit methods in number theory was organised by karim. The range of topics includes the satotate conjecure, langlands programme, function. Advanced topics in computational number theory, graduate texts in math. The queen of mathematics gauss wrote that \mathematics is the queen of sciences and. Number theory see also adam epstein alex bartel is willing to supervise one or two projects in the field of algebraic number theory.
An important aspect of the course was the final project. Number theory and algebraic geometry, british mathematical colloquium, university of kent, 1718 april, 2012. Uniform bounds for the number of rational points on curves of small mordellweil rank katz, eric, rabinoff, joseph, and zureickbrown, david, duke mathematical journal, 2016. Introduction to abstract algebra by samir siksek download book. Additional information the firstnamed author is supported through a grant within the framework of the dfg priority programme 1489 algorithmic and experimental methods in algebra, geometry and number theory. Topics in number theory, proceedings of a conference in honor of b. Samir siksek let k be a number field, x a smooth curve over k, and f a nonconstant element of the function field k x. Boston collegemit number theory seminar founder and coorganizer. Equidistribution, lfunctions and ergodic theory 3 which identi.
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