Dr Frazer Jarvis
School of Mathematical and Physical Sciences
Mathematics Programme Lead
Reader in Pure Mathematics
Full contact details
School of Mathematical and Physical Sciences
J12
Hicks Building
Hounsfield Road
ºù«Ӱҵ
S3 7RH
- Research interests
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Dr Jarvis works in the area of algebraic number theory, an area which uses techniques from algebra, algebraic geometry and classical number theory, amongst others. In particular, he studies the relationship between modular forms, elliptic curves and representations of Galois groups. That this is currently an active area of research is clear from the recent proof of Fermat's Last Theorem by Andrew Wiles; Wiles uses exactly these methods in his proof. Dr Jarvis is particularly interested in generalisations of these ideas (known as the Langlands Philosophy), and even in possible generalisations of Fermat's Last Theorem. For example, one might ask whether the Fermat equation of a given degree (or a similar equation) has solutions in a given field extension of the rationals. Within this speciality, there are a number of possible research topics.
- Publications
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Show: Featured publications All publications
Featured publications
Journal articles
- . Ramanujan Journal.
- . Journal of Number Theory, 199, 251-288.
- Fermat's Last Theorem over Q(√2, (√3). Algebra & Number Theory.
All publications
Books
- . Springer.
Journal articles
- . Ramanujan Journal.
- . Journal of Number Theory, 199, 251-288.
- Some factorisation and divisibility properties of Catalan polynomials. Bulletin of the Institute of Combinatorics and its Applications, 71, 36-56.
- Convergence of Iterated Generating Functions. Bull. Inst. Combin. Appl., 71, 70-76.
- . Glasgow Mathematical Journal, 55, 309-312.
- . The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanu, 22, 171-186.
- . Duke Mathematical Journal, 155, 105-161.
- . JOURNAL OF NUMBER THEORY, 128(3), 589-618.
- On the modularity of supersingular elliptic curves over certain totally real number fields. Journal of Number Theory, 128, 589-618.
- . The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanu, 17, 1-17.
- A short proof of the 2-adic valuation
of the Catalan-Larcombe-French number. Indian Journal of Mathematics, 48, 135-138.
- Optimal levels for modular mod 2 representations over totally real fields. Documenta Mathematica, Extra volume: John Coates 60th birthday, 533-550.
- Mathematics of Sudoku I. Mathematical Spectrum, 39, 15-22.
- Mathematics of Sudoku II. Mathematical Spectrum, 39, 54-58.
- Square roots by subtraction. Mathematical Spectrum, 37, 119-122.
- On small prime divisibility of the
Catalan-Larcombe-French sequence. Indian Journal of Mathematics, 47, 159-181.
- Power series identities generated by
two recent integer sequences. Bulletin of the Institute of Combinatorics and its Applications, 43, 85-95.
- Linear recurrences between two recent
integer sequences. Congressus Numerantium: a conference journal on numerical themes, 169, 79-99.
- Correspondences on Shimura curves and Mazur’s Principle at p. Pacific Journal of Mathematics, 213, 267-280.
- . Journal of Number Theory, 109(1), 182-196.
- The generating function for the Catalan numbers. Mathematical Spectrum, 36, 9-12.
- Applications of the AGM of Gauss:
some new properties of the Catalan-Larcombe-French sequence. Congressus Numerantium: a conference journal on numerical themes, 161, 151-162.
- . Bulletin of the London Mathematical Society, 33(2), 252-253.
- An elementary proof of a distribution relation on elliptic curves. Manuscripta Mathematica, 103, 329-337.
- . Bulletin of the London Mathematical Society, 32, 146-154.
- . Compositio Mathematica, 116, 39-79.
- Level lowering for modular mod l representations over totally real fields. Mathematische Annalen, 313, 141-160.
- On Galois representations associated to Hilbert modular forms. Journal fuer die Reine und Angewandte Mathematik: Crelle's journal, 491, 199-216.
- Fermat's Last Theorem over Q(√2, (√3). Algebra & Number Theory.
Preprints
- , arXiv.
- . Ramanujan Journal.
- Research group
- Grants
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Past grants, as Principal Investigator
EPSRC
- Teaching activities
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MAS111 Mathematics Core II MAS369 Machine Learning MAS61007 Machine learning
Links