Published

  • Triple sums of Kloosterman sums and the discrepancy of modular inverses
    Joint with V. Blomer and I. E. Shparlinski
    arXiv, 2024, 27 pages, submitted for publication.

  • Counting and equidistribution over primes in hyperbolic groups
    Joint with Y. Petridis
    arXiv, 2024, 32 pages,
    accepted for publication in Commentarii Mathematici Helvetici, 2024

  • The distribution of Manin’s iterated integrals of modular forms
    Joint with N. Matthes
    arXiv/final J. Reine Angew. Math. 812 (2024), 125–161

  • Bounds on shifted convolution sums for Hecke eigenforms
    Joint with Y. Petridis and A. C. Nordentoft
    arXiv/final
    Res. number theory 8, 26 (2022)

  • Small scale equidistribution of Hecke eigenforms at infinity
    Joint with Y. Petridis and A. C. Nordentoft
    arXiv/final
    J. London Math. Soc. (2) 2022;106:2696–2729

  • Prime geodesics and averages of the Zagier L-series
    Joint with O. Balkanova and D. Frolenkov
    arXiv/final
    Math. Proc. Cambridge Philos. Soc, 172(3), 705-728 (2022)

  • Higher order deformations of hyperbolic spectra
    Joint with Y. Petridis
    arXiv, 16 pages
    In S. Albeverio, A. Balslev, R. Weder (Eds.)
    Schrödinger Operators, Spectral Analysis and Number Theory,
    In Memory of Erik Balslev, 2021, Springer Verlag

  • Averaging over Heegner points in the hyperbolic circle problem
    Joint with Y. Petridis
    arXiv/final
    International Mathematics Research Notices 2018, 16:4942–4968

  • Arithmetic statistics of modular symbols
    Joint with Y. Petridis
    arXiv/final
    Inventiones Mathematicae 212 (2018), no. 3, pp 997–1053

  • On the variance of the error term in the hyperbolic circle problem
    Joint with G. Cherubini
    arXiv/final
    Revista Matemática Iberoamericana 34 (2018), no. 2, 655–685

  • Angles in hyperbolic lattices: The pair correlation density
    Joint with A. Södergren
    arXiv/final
    Trans. Amer. Math. Soc. 369 (2017), 2807-2841

  • Local average in hyperbolic lattice point counting
    With appendix by N. Laaksonen
    Joint with Y. Petridis
    arXiv/final
    Math. Z. 285 (2017), no. 3-4, 1319–1344

  • Double Dirichlet series and quantum unique ergodicity of weight one-half Eisenstein series
    Joint with Y. Petridis and N. Raulf
    arXiv/final
    Algebra & Number Theory 8(7):1539–1595 (2014)

  • Dissolving cusp forms: Higher order Fermi’s Golden Rules
    Joint with Y. Petridis
    arXiv/final
    Mathematika 59 (2013), no. 2, 269-301

  • Quantum limits of Eisenstein series and scattering states
    Joint with Y. Petridis and N. Raulf
    arXiv/final
    Canad. Math. Bull. 56(4):814–826 (2013)
    Erratum

  • Non-vanishing of Taylor coefficients and Poincaré series
    Joint with Cormac O’Sullivan
    arXiv/final
    Ramanujan Journal 30 (2013), no. 1, 67-100

  • Instability of cuspidal eigenvalues for hyperbolic surfaces
    Joint with Y. Petridis
    PDF
    In Automorphic forms, trace formulas and zeta functions (ed. Y. Gon and T. Moriyama),
    volume 1767, pages 146–160. RIMS Kôkyûroku, 2011

  • On Selberg’s small eigenvalue conjecture and residual eigenvalues
    arXiv/final
    Journal für die reine und angewandte Mathematik 656 (2011), 179–211

  • Pairs of periodic orbits with fixed homology difference
    Joint with R. Sharp
    arXiv/final
    Proc. Edinb. Math. Soc. (2) 53(3): 799–808 (2010)

  • Hyperbolic lattice-point counting and modular symbols
    Joint with Y. Petridis
    arXiv/final
    Journal de Théorie des Nombres de Bordeaux 21 (2009), 719-732

  • Distribution of Angles in Hyperbolic Lattices
    Joint with J. L. Truelsen
    arXiv/final
    Quarterly Journal of Mathematics 61(1):117-133 (2010)

  • On the statistics of the minimal solution of a linear Diophantine equation and uniform distribution of the real part of orbits in hyperbolic spaces
    Joint with Z. Rudnick
    arXiv
    In Spectral analysis in geometry and number theory, volume 484 of Contemporary Math,
    pages 187-194, Amer. Math. Soc, Providence, RI, 2009

  • Equidistribution of geodesics on homology classes and analogues for free groups
    Joint with Y. N. Petridis
    arXiv/final
    Forum Mathematicum 20(5):783–815 (2008)

  • Discrete logarithms in free groups
    Joint with Y. N. Petridis
    arXiv/final
    Proceedings of the American Mathematical Society 134 (2006), 1003-1012

  • The distribution of values of the Poincare pairing for hyperbolic Riemann surfaces
    Joint with Y. N. Petridis
    arXiv/final
    Journal für die Reine und Angewandte Mathematik 579 (2005), 159-173

  • Distribution of modular symbols for compact surfaces
    arXiv/final
    International Mathematics Research Notices 2004, no. 41, 2125-2146

  • Modular symbols have a normal distribution
    Joint with Y. N. Petridis
    arXiv/final
    Geometric and Functional Analysis 14 (2004), no. 5, 1013–1043

  • Asymptotic densities of newforms
    arXiv/final
    Journal of Number Theory 109 (2004), no. 1, 96-119

Unpublished