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Research
- Preprints by members of the research group
- Algebraic and Analytic Methods in Number Theory (EPSRC grant no. EP/F060661/1)
- Rational Points on Algebraic Varieties (EPSRC grant no. GR/R93155/01)
- Papers by members of the group, on the departmental eprint server
Seminars
- Number theory seminars
- Next seminar: 24 October 201916:00Javier FresánAbstract
Guided by the analogy with certain moments of the Bessel function that appear as Feynman integrals, Broadhurst and Roberts recently studied a family of L-functions built up by assembling symmetric power moments of Kloosterman sums over finite fields. I will prove that these L-functions arise from potentially automorphic motives over the field of rational numbers, and hence admit a meromorphic continuation to the complex plane that satisfies the expected functional equation. If time permits, I will identify the periods of the corresponding motives with the Bessel moments and make a few comments about the special values of the L-functions. This is a joint work with Claude Sabbah and Jeng-Daw Yu.
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- Junior number theory seminars
- Next seminar: Tomorrow16:00Konstantinos KartasAbstract
The goal of the talk is to present a proof of the following statement:
Let (K,v) be an algebraic extension of (Q_p,v_p). We show that K is relatively decidable to its tilt K^♭, i.e. if K^♭ is decidable in the language of valued fields, then so is K.
In the first part [of the talk], I will try to cover the necessary background needed from model theory and the theory of perfectoid fields.
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