Research
I'm interested in Analytic Number Theory and more specifically in moments of L-functions and in related problems.
During my first year, I worked on the shifted second moment of the Riemann zeta-function, extending a theorem of Ingham to the case where the shifts are unbounded in the imaginary direction. I published the result I obtained in a paper called The second shifted moment of the Riemann zeta function (Int. J. Number Theory 6 (2010), no. 8, 1933–1944). More recently, I have also been working on analogous results for other families of L-functions.
During the last year, I have been working with Brian Conrey on some properties of the Eisenstein series. From these, we were able to deduce a reciprocity formula for the Vasyunin sum (and for some other "cotangent sums"). Also, we proved an exact formula for a smooth version of the second moment of the Riemann zeta-function, expressing this average in terms of a series that is both asymptotic and convergent. You can find on this paper some of the results we have achieved.
