Dr Frazer Jarvis

School of Mathematical and Physical Sciences

Mathematics Programme Lead

Reader in Pure Mathematics

a.f.jarvis@sheffield.ac.uk
J12, Hicks Building

Full contact details

Dr Frazer Jarvis
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

Journal articles

  • Khawaja M & Jarvis A (2025) . Algebra & Number Theory, 19(3), 457-480.
  • Chow R & Jarvis AF (2023) . Ramanujan Journal, 61(3), 935-956.
  • Tsaltas K & Jarvis AF (2019) . Journal of Number Theory, 199, 251-288.

All publications

Books

  • Jarvis AF (2014) . Springer.

Journal articles

  • Khawaja M & Jarvis A (2025) . Algebra & Number Theory, 19(3), 457-480.
  • Chow R & Jarvis AF (2023) . Ramanujan Journal, 61(3), 935-956.
  • Tsaltas K & Jarvis AF (2019) . Journal of Number Theory, 199, 251-288.
  • Jarvis AF, Larcombe P & Fennessey E (2014) Some factorisation and divisibility properties of Catalan polynomials. Bulletin of the Institute of Combinatorics and its Applications, 71, 36-56.
  • Jarvis AF (2014) Convergence of Iterated Generating Functions. Bull. Inst. Combin. Appl., 71, 70-76.
  • Jarvis AF (2013) . Glasgow Mathematical Journal, 55, 309-312.
  • Jarvis AF & Verrill H (2010) . The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanu, 22, 171-186.
  • Jarvis AF, Buzzard KM & Diamond F (2010) . Duke Mathematical Journal, 155, 105-161.
  • Jarvis F & Manoharmayum J (2008) . JOURNAL OF NUMBER THEORY, 128(3), 589-618.
  • Jarvis AF & Manoharmayum J (2008) On the modularity of supersingular elliptic curves over certain totally real number fields. Journal of Number Theory, 128, 589-618.
  • Jarvis AF (2008) . The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanu, 17, 1-17.
  • Jarvis AF, French D & Larcombe P (2006) A short proof of the 2-adic valuation of the Catalan-Larcombe-French number. Indian Journal of Mathematics, 48, 135-138.
  • Jarvis AF (2006) Optimal levels for modular mod 2 representations over totally real fields. Documenta Mathematica, Extra volume: John Coates 60th birthday, 533-550.
  • Jarvis AF & Felgenhauer B (2006) Mathematics of Sudoku I. Mathematical Spectrum, 39, 15-22.
  • Jarvis AF & Russell E (2006) Mathematics of Sudoku II. Mathematical Spectrum, 39, 54-58.
  • Jarvis AF (2005) Square roots by subtraction. Mathematical Spectrum, 37, 119-122.
  • Jarvis AF, French D & Larcombe P (2005) On small prime divisibility of the Catalan-Larcombe-French sequence. Indian Journal of Mathematics, 47, 159-181.
  • Jarvis AF, French D & Larcombe P (2005) Power series identities generated by two recent integer sequences. Bulletin of the Institute of Combinatorics and its Applications, 43, 85-95.
  • Jarvis AF, French D & Larcombe P (2004) Linear recurrences between two recent integer sequences. Congressus Numerantium: a conference journal on numerical themes, 169, 79-99.
  • Jarvis AF (2004) Correspondences on Shimura curves and Mazur’s Principle at p. Pacific Journal of Mathematics, 213, 267-280.
  • Jarvis F & Meekin P (2004) . Journal of Number Theory, 109(1), 182-196.
  • Jarvis AF (2003) The generating function for the Catalan numbers. Mathematical Spectrum, 36, 9-12.
  • Jarvis AF, French D & Larcombe P (2003) 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.
  • Jarvis F (2001) . Bulletin of the London Mathematical Society, 33(2), 252-253.
  • Jarvis AF (2000) An elementary proof of a distribution relation on elliptic curves. Manuscripta Mathematica, 103, 329-337.
  • Jarvis AF (2000) . Bulletin of the London Mathematical Society, 32, 146-154.
  • Jarvis AF (1999) . Compositio Mathematica, 116, 39-79.
  • Jarvis AF (1999) Level lowering for modular mod l representations over totally real fields. Mathematische Annalen, 313, 141-160.
  • Jarvis AF (1997) On Galois representations associated to Hilbert modular forms. Journal fuer die Reine und Angewandte Mathematik: Crelle's journal, 491, 199-216.

Preprints

  • Jarvis F & Manoharmayum J (2007) , arXiv.
Research group

Grants

Past grants, as Principal Investigator
EPSRC
Teaching activities
MAS111 Mathematics Core II
MAS369 Machine Learning
MAS61007 Machine learning

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