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University of Oxford
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A conjectural extension of Hecke’s converse theorem
The Ramanujan Journal (10 November 2017)
I'm interested in the analytic properties of L-functions. In particular:
- How are they established? My recent research is concerned with extensions of the Langlands--Shahidi method;
- What do they mean? I am very interested in so-called "converse theorems" (they are converse to the well-known fact that if V is an automorphic representation, then L(V,s) has nice analytic properties).
My latest work studies the orders of and cancellation between zeros of L-functions. In particular:
- Constraints on the orders of non-real zeros (which are expected to be simple);
- Poles of quotients of L-functions.
Prizes, Awards, and Scholarships:
- LMS grant scheme 4 - "Research in pairs", joint with Michalis Neururer.
- HIMR focused research grant (2016) - "Kac--Moody groups and L-functions", joint with Sergey Oblezin.
- LMS grant scheme 1 (2016) - "Algebraisation and geometrisation in the Langlands programme", joint with Robert Kurinczuk.
- University of Nottingham: Graduate school travel prize (2014).
- University of Durham: Collingwood memorial prize (2010); Charles Holmes prize (2010); Nuffield Foundation undergraduate research bursary (2009); Norton prize (2008).
Major / Recent Publications:
- "A conjectural extension of Hecke's converse theorem", joint with S. Bettin, J.W.Bober, A.R. Booker, B. Conrey, M. Lee, G. Molteni, T. Oliver, D.J. Platt, R.S. Steiner. To appear in the Ramanujan journal. arXiv:1704.02570.
- "Notes on low degree L-data", survey article for RIMS Kôkyûroku, no. 2014, "Analytic Number Theory and Related Areas". arXiv:1601.05009.