Dr Frazer Jarvis
School of Mathematical and Physical Sciences
Mathematics Programme Lead
Reader in Pure Mathematics
+44 114 222 3845
Full contact details
School of Mathematical and Physical Sciences
J12
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
- Research interests
-
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
-
Show: Featured publications All publications
Featured publications
Journal articles
- A p-adic study of the Richelot isogeny with applications to periods of certain genus 2 curves. Ramanujan Journal.
- Descending congruences of theta lifts on GSp4. Journal of Number Theory, 199, 251-288. View this article in WRRO
All publications
Books
- Algebraic Number Theory. Springer.
Journal articles
- A p-adic study of the Richelot isogeny with applications to periods of certain genus 2 curves. Ramanujan Journal.
- Descending congruences of theta lifts on GSp4. Journal of Number Theory, 199, 251-288. View this article in WRRO
- 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.
- On a pairing between symmetric power modules. Glasgow Mathematical Journal, 55, 309-312.
- Supercongruences for the Catalan-Larcombe-French
numbers. The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanu, 22, 171-186.
- On Serre's conjecture for mod l
Galois representations over totally real fields. Duke Mathematical Journal, 155, 105-161.
- On the modularity of supersingular elliptic curves over certain totally real number fields. 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.
- Higher genus arithmetic-geometric means. 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.
- The Fermat equation over ℚ (2). 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.
- COHOMOLOGY OF NUMBER FIELDS (Grundlehren der Mathematischen Wissenschaften 323). 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.
- A distribution relation on elliptic curves. Bulletin of the London Mathematical Society, 32, 146-154.
- Mazur’s Principle for totally real fields of odd degree. 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.
Preprints
- A p-adic study of the Richelot isogeny with applications to periods of certain genus 2 curves. Ramanujan Journal.
- Research group
- Grants
-
Past grants, as Principal Investigator
Modularity of elliptic curves over totally real fields EPSRC
- Teaching activities
-
MAS111 Mathematics Core II MAS369 Machine Learning MAS61007 Machine learning