Dr Frazer Jarvis

School of Mathematics and Statistics

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Programme Level Lead

A.F.Jarvis@shef.ac.uk
+44 114 222 3845

Full contact details

Dr Frazer Jarvis
School of Mathematics and Statistics
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

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Journal articles

All publications

Books

Journal articles

  • Tsaltas K & Jarvis AF (2019) Descending congruences of theta lifts on GSp4. Journal of Number Theory, 199, 251-288. View this article in WRRO RIS download Bibtex download
  • Jarvis AF & Tsaltas K (2019) Descending congruences of theta lifts on GSp(4). Journal of Number Theory, 199, 251-288. RIS download Bibtex download
  • 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. RIS download Bibtex download
  • Jarvis AF (2014) Convergence of Iterated Generating Functions. Bull. Inst. Combin. Appl., 71, 70-76. RIS download Bibtex download
  • Jarvis AF (2013) On a pairing between symmetric power modules. Glasgow Mathematical Journal, 55, 309-312. RIS download Bibtex download
  • Jarvis AF & Verrill H (2010) Supercongruences for the Catalan-Larcombe-French numbers. The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanu, 22, 171-186. RIS download Bibtex download
  • Jarvis AF, Buzzard KM & Diamond F (2010) On Serre's conjecture for mod l Galois representations over totally real fields. Duke Mathematical Journal, 155, 105-161. RIS download Bibtex download
  • Jarvis F & Manoharmayum J (2008) On the modularity of supersingular elliptic curves over certain totally real number fields. JOURNAL OF NUMBER THEORY, 128(3), 589-618. RIS download Bibtex download
  • 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. RIS download Bibtex download
  • Jarvis AF (2008) Higher genus arithmetic-geometric means. The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanu, 17, 1-17. RIS download Bibtex download
  • 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. RIS download Bibtex download
  • Jarvis AF (2006) Optimal levels for modular mod 2 representations over totally real fields. Documenta Mathematica, Extra volume: John Coates 60th birthday, 533-550. RIS download Bibtex download
  • Jarvis AF & Felgenhauer B (2006) Mathematics of Sudoku I. Mathematical Spectrum, 39, 15-22. RIS download Bibtex download
  • Jarvis AF & Russell E (2006) Mathematics of Sudoku II. Mathematical Spectrum, 39, 54-58. RIS download Bibtex download
  • Jarvis AF (2005) Square roots by subtraction. Mathematical Spectrum, 37, 119-122. RIS download Bibtex download
  • Jarvis AF, French D & Larcombe P (2005) On small prime divisibility of the Catalan-Larcombe-French sequence. Indian Journal of Mathematics, 47, 159-181. RIS download Bibtex download
  • 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. RIS download Bibtex download
  • 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. RIS download Bibtex download
  • Jarvis AF (2004) Correspondences on Shimura curves and Mazur’s Principle at p. Pacific Journal of Mathematics, 213, 267-280. RIS download Bibtex download
  • Jarvis F & Meekin P (2004) The Fermat equation over ℚ (2). Journal of Number Theory, 109(1), 182-196. RIS download Bibtex download
  • Jarvis AF (2003) The generating function for the Catalan numbers. Mathematical Spectrum, 36, 9-12. RIS download Bibtex download
  • 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. RIS download Bibtex download
  • Jarvis F (2001) COHOMOLOGY OF NUMBER FIELDS (Grundlehren der Mathematischen Wissenschaften 323). Bulletin of the London Mathematical Society, 33(2), 252-253. RIS download Bibtex download
  • Jarvis AF (2000) An elementary proof of a distribution relation on elliptic curves. Manuscripta Mathematica, 103, 329-337. RIS download Bibtex download
  • Jarvis AF (2000) A distribution relation on elliptic curves. Bulletin of the London Mathematical Society, 32, 146-154. RIS download Bibtex download
  • Jarvis AF (1999) Mazur’s Principle for totally real fields of odd degree. Compositio Mathematica, 116, 39-79. RIS download Bibtex download
  • Jarvis AF (1999) Level lowering for modular mod l representations over totally real fields. Mathematische Annalen, 313, 141-160. RIS download Bibtex download
  • Jarvis AF (1997) On Galois representations associated to Hilbert modular forms. Journal fuer die Reine und Angewandte Mathematik: Crelle's journal, 491, 199-216. RIS download Bibtex download
Research group

Number Theory

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