Publications

  1. Arithmetic statistics of modular symbols, joint with Y. Petridis, 43 pages, 2017, arXiv. Preprint
  2. Averaging over Heegner points in the hyperbolic circle problem, joint with Y. Petridis, 20 pages, arXiv. Accepted for publication in International Mathematics Research Notices
  3. On the variance of the error term in the hyperbolic circle problem. joint with Giacomo Cherubini 26 pages, arXiv. Accepted for publication in Reviste Matemática Iberoamericana.
  4. Angles in hyperbolic lattices : The pair correlation density. joint with Anders Södergren, arXiv/final, Trans. Amer. Math. Soc. 369 (2017), 2807-2841
  5. Local average in hyperbolic lattice point counting, with an appendix by Niko Laaksonen.  joint with Y. Petridis.  arXiv/finalMath. Z. 285 (2017), no. 3-4, 1319–1344.
  6. Double Dirichlet series and quantum unique ergodicity of weight one-half Eisenstein series.  joint with Y. Petridis and N. Raulf. 45 arXiv/final, Algebra & Number Theory, 8(7):1539–1595, 2014.
  7. Dissolving cusp forms: Higher order Fermi’s Golden Rules, joint with Y. PetridisarXiv/final  Mathematika, 2013, Vol 59 (2),  269-301
  8. Quantum limits of Eisenstein series and scattering states, joint with Y. Petridis and N. RaulfarXiv/final Canad. Math. Bull., 56(4):814–826, 2013.,2013, 814-826./Erratum.
  9. Non-vanishing of Taylor coefficients and Poincaré series, joint with Cormac O’SullivanarXiv/final Ramanujan Journal, 2013, Volume 30, Issue 1, pp 67-100.
  10. 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.
  11. On Selberg’s small eigenvalue conjecture and residual eigenvalues. arXiv /final Journal für die reine und angewandte Mathematik. 2011, 656,  179–211
  12. Pairs of periodic orbits with fixed homology difference , joint with R. Sharp. arXiv /final Proc. Edinb. Math. Soc. (2), 53(3): 799–808, 2010.
  13. Hyperbolic lattice-point counting and modular symbols, joint with Y. Petridis. arXiv/final Journal de Théorie des Nombres de Bordeaux. 21 (2009), 719-732
  14. Distribution of Angles in Hyperbolic Lattices, joint with J. L. Truelsen.arXiv/final Quaterly Journal of Mathematics. 2010 61(1):117-133
  15. 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
  16. 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.
  17. Discrete logarithms in free groups, joint with Y. N. Petridis. arXiv/final Proceedings of the American Mathematical Society, 2006, 134, 1003-1012.
  18. 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 2005 579, 159-173
  19. Distribution of modular symbols for compact surfaces. arXiv/final International Mathematics Research Notices 2004, nr. 41, p. 2125-2146
  20. Modular symbols have a normal distribution, joint with Y. N. Petridis. arXiv/final Geometric and Functional Analysis 14 (2004), no. 5, p. 1013 – 1043
  21. Asymptotic densities of newforms. arXiv/final Journal of Number Theory, 109 (2004), no. 1, p. 96-119

Unpublished

  1. On pairs of prime geodesics with fixed homology difference. 2006 arXiv
  2. Automorphic forms and modular symbols. PhD thesis supervised by E. Balslev and A. B. Venkov, University of Aarhus, Feb 2003.