Notes
On some geometric probabilities, notes from 2024 [pdf]
Fermat's two squares theorem and quartic residuacity, notes from 2024 written jointly with Roland Bacher [pdf]
An interesting indefinite integral quadratic form, notes from 2024 [pdf]
On the sum of two coprime squares, notes from 2023 [pdf]
A new zero-free region for Rankin-Selberg L-functions, Oberwolfach report of a lecture given in 2023 [pdf]
The reciprocity of Gauss sums via the residue theorem, notes from 2023 [pdf]
The Lee-Yang circle theorem, notes from 2022 [pdf]
Stirling's approximation, notes from 2021 [pdf]
The Bombieri-Halász-Montgomery inequality, notes from 2021 [pdf]
Selberg's identity for Kloosterman sums, unpublished manuscript from 2017 written jointly with Gyula Károlyi [pdf]
The prime geodesic theorem (after Soundararajan and Young), scanned notes (5 MB) for three lectures given at Alfréd Rényi Institute of Mathematics in 2017 [pdf]
Kvantumkáosz és számelmélet [Hungarian], scanned notes (2 MB) for two lectures given at Budapest University of Technology and Economics in 2016 [pdf]
On the hybrid moments of the generalized divisor function, notes from 2016 [pdf]
Weil's bound for Kloosterman sums, notes from 2015 [pdf]
On the monotonicity of Dirichlet's eta function, notes from 2014 [pdf]
A 2-adic approach to the Ramanujan-Nagell equation, unpublished manuscript from 2013 [pdf]
The additive and multiplicative large sieve inequality, notes from 2013 [pdf]
L-functions and equidistribution, scanned notes (17 MB) for a lecture series given at Georg-August-Universität Göttingen in 2012 [pdf]
On the sup-norm of Maass cusp forms of large level, Oberwolfach report of a lecture given in 2011 [pdf]
On the cusps of Γ(q) and Γ0(q), notes for a course given at Central European University in 2009 [pdf]
A set of representatives for Γ0(q)\SL2(ℤ), notes for a course given at Central European University in 2009 [pdf]
Basic L-functions, notes for a lecture given at Central European University in 2009 [pdf]
A special cubic modulo primes, notes for a lecture given at Lauder Javne Jewish Community School in 2009 [pdf]; Lecture outline [pdf]
The spectral decomposition of shifted convolution sums, notes for a lecture given at Bristol University and the University of Oxford in 2007 [pdf]
Additív konvolúciós összegek spektrális felbontása [Hungarian], notes for a lecture given at Rényi Institute in 2007 [pdf]
Introduction to number theory, notes for a one-semester course taught in 2005 at the University of Texas in Austin [pdf]
On a result of András Biró, unpublished manuscript from 2000 [pdf]
Note on fully characteristic submodules over principal ideal domains, unpublished manuscript from 1994 [pdf]