Publications

  1. Counting and equidistribution over primes in hyperbolic groups, joint with Y. Petridis,  arXiv, 32 pages, Accepted for publication in Commentarii Mathematici Helvetici, 2024
  2. The distribution of Manin’s iterated integrals of modular forms, joint with N. Matthes  arXiv, J. Reine Angew. Math. 812 (2024), 125–161.
  3. Bounds on shifted convolution sums for Hecke eigenforms, joint with Y. Petridis and A. C. Nordentoft  arXiv/final Res. number theory 8, 26 (2022).
  4. 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.
  5. Prime geodesics and averages of the Zagier L-series,  joint with O. Balkanova and D. Frolenkov, 24 pages, arXiv/final, Math. Proc. Cambridge Philos. Soc, 172(3), 705-728. 2022
  6. Higher order deformations of hyperbolic spectra, arXiv, joint with Y. Petridis, 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
  7. Averaging over Heegner points in the hyperbolic circle problem, joint with Y. Petridis, 27 pages, arXiv/final. International Mathematics Research Notices, Volume 2018 Issue 16, August, Pages 4942–4968
  8. Arithmetic statistics of modular symbols, joint with Y. Petridis, 57 pages, arXiv/final, Inventiones Mathematicae , June 2018, Volume 212, Issue 3, pp 997–1053
  9. On the variance of the error term in the hyperbolic circle problem. joint with G. Cherubini 26 pages, arXiv/final. Reviste Matemática Iberoamericana. Vol. 34, 2018, no. 2, 655–685.
  10. Angles in hyperbolic lattices : The pair correlation density. joint with A. Södergren, arXiv/final, Trans. Amer. Math. Soc. 369 (2017), 2807-2841
  11. Local average in hyperbolic lattice point counting, with an appendix by N. Laaksonen.  joint with Y. Petridis.  arXiv/final, Math. Z. 285 (2017), no. 3-4, 1319–1344.
  12. 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.
  13. Dissolving cusp forms: Higher order Fermi’s Golden Rules, joint with Y. Petridis. arXiv/final  Mathematika, 2013, Vol 59 (2),  269-301
  14. 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.,2013, 814-826./Erratum.
  15. Non-vanishing of Taylor coefficients and Poincaré series, joint with Cormac O’Sullivan. arXiv/final Ramanujan Journal, 2013, Volume 30, Issue 1, pp 67-100.
  16. 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.
  17. On Selberg’s small eigenvalue conjecture and residual eigenvalues. arXiv /final Journal für die reine und angewandte Mathematik. 2011, 656,  179–211
  18. Pairs of periodic orbits with fixed homology difference , joint with R. Sharp. arXiv /final Proc. Edinb. Math. Soc. (2), 53(3): 799–808, 2010.
  19. Hyperbolic lattice-point counting and modular symbols, joint with Y. Petridis. arXiv/final Journal de Théorie des Nombres de Bordeaux. 21 (2009), 719-732
  20. Distribution of Angles in Hyperbolic Lattices, joint with J. L. Truelsen.arXiv/final Quaterly Journal of Mathematics. 2010 61(1):117-133
  21. 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
  22. 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.
  23. Discrete logarithms in free groups, joint with Y. N. Petridis. arXiv/final Proceedings of the American Mathematical Society, 2006, 134, 1003-1012.
  24. 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
  25. Distribution of modular symbols for compact surfaces. arXiv/final International Mathematics Research Notices 2004, nr. 41, p. 2125-2146
  26. Modular symbols have a normal distribution, joint with Y. N. Petridis. arXiv/final Geometric and Functional Analysis 14 (2004), no. 5, p. 1013 – 1043
  27. Asymptotic densities of newforms. arXiv/final Journal of Number Theory, 109 (2004), no. 1, p. 96-119

Unpublished

  1. Introduction to number theory Lecture notes. 79 pages, 2020
  2. On pairs of prime geodesics with fixed homology difference. 2006 arXiv
  3. Automorphic forms and modular symbols. PhD thesis supervised by E. Balslev and A. B. Venkov, University of Aarhus, Feb 2003.