Esa V. Vesalainen


Refereed research articles

  1. (with A.-M. Ernvall-Hytönen) On fourth and higher moments of short exponential sums related to cusp forms, Journal of Number Theory, 218 (2021), 180–208.
  2. (with E. Blåsten) Non-scattering energies and transmission eigenvalues in Hn, Annales Academiæ Scientiarum Fennicæ Mathematica, 45 (2020), 547–576.
  3. (with J. Jääsaari) Exponential sums related to Maass forms, Acta Arithmetica, 190 (2019), 1–48.
  4. (with A.-M. Ernvall-Hytönen) On the secrecy gain of l-modular lattices, SIAM Journal on Discrete Mathematics, 32 (2018), 1441–1457.
  5. (with A.-M. Ernvall-Hytönen) On a conjecture of Faulhuber and Steinerberger on the logarithmic derivative of ϑ4, Comptes Rendus Mathématique, 356 (2018), 457–462.
  6. (with J. Jääsaari) On sums involving Fourier coefficients of Maass forms for SL(3, Z), Functiones et Approximatio Commentarii Mathematici, 57 (2017), 255–275. Correction.
  7. (with L. Päivärinta and M. Salo) Strictly convex corners scatter, Revista Matemática Iberoamericana, 33 (2017), 1369–1396.
  8. Moments and oscillations of exponential sums related to cusp forms, Mathematical Proceedings of the Cambridge Philosophical Society, 162 (2017), 479–506.
  9. (with A. García and M. Zubeldia) Discreteness of transmission eigenvalues for higher-order main terms and perturbations, SIAM Journal on Mathematical Analysis, 48 (2016), 2382–2398.
  10. (with G. Hu and M. Salo) Shape identification in inverse medium scattering problems with a single far-field pattern, SIAM Journal on Mathematical Analysis, 48 (2016), 152–165.
  11. (with A.-M. Ernvall-Hytönen and J. Jääsaari) Resonances and Ω-results for exponential sums related to Maass forms for SL(nZ), Journal of Number Theory, 153 (2015), 135–157.
  12. Rellich type theorems for unbounded domains, Inverse Problems and Imaging, 8 (2014), 865–883.
  13. Transmission eigenvalues for a class of non-compactly supported potentials, Inverse Problems, 29 (2013), 104006, 1–11.

Popular texts

  1. Muirheadin epäyhtälö: ongelmien ratkaisuita (Muirhead’s inequality: solutions to problems, in Finnish), Solmu, 1/2020, 11–13.
  2. Muirheadin epäyhtälö (Muirhead’s inequality, in Finnish), Solmu, 3/2019, 23–33.
  3. Kolmannen ja neljännen asteen yhtälöistä (On equations of third and fourth degree, in Finnish), Solmu, 2/2019, 7–11.
  4. Kahden muuttujan keskiarvoista (On means of two variables, in Finnish), Solmu, 1/2019, 11–14.
  5. Transkendenttiluvut ja Hermiten lause (Transcendental numbers and Hermite’s theorem, in Finnish), Solmu, 3/2018, 12–22.
  6. Moniulotteisuuden ihmeitä: ongelmien ratkaisuita (Wonders of multidimensionality: solutions to problems, in Finnish), Solmu, 2/2018, 32–33.
  7. Moniulotteisuuden ihmeitä: Shapiron syklinen epäyhtälö (Wonders of multidimensionality: Shapiro’s cyclic inequality, in Finnish), Solmu, 1/2018, 26–34.
  8. Miksi kahden negatiivisen luvun tulo on positiivinen? (Why the product of two negative numbers is positive?, in Finnish), Solmu, 2/2017, 41–42.
  9. Modulimuodot: lukuteorian aarteita (Modular forms: treasures of number theory, in Finnish), Arkhimedes, 4/2016, 9–19.
  10. 57. kansainväliset matematiikkaolympialaiset Hongkongissa (57th International Mathematical Olympiad in Hong Kong, in Finnish), Solmu, 3/2016, 20–25.
  11. Tasograafit ja väritykset: ratkaisuita ongelmiin (Planar graphs and colourings: solutions to problems, in Finnish), Solmu, 2/2016, 13–15.
  12. Tasograafit ja väritykset (Planar graphs and colourings, in Finnish), Solmu, 1/2016, 7–13.
  13. (with M. Kauppila) Euroopan tyttöjen matematiikkaolympialaiset Minskissä 14.–20.4.2015 (The European Girls’ Mathematical Olympiad in Minsk, 14–20 April, 2015, in Finnish), Solmu, 3/2015, 19–23.
  14. (with K. Kulmala) Riemannin ζ-funktio (Riemann’s ζ-function, in Finnish), Solmu, 1/2015, 23–29.
  15. (with A.-M. Ernvall-Hytönen and M. Kauppila) Euroopan tyttöjen matematiikkaolympialaiset Antalyassa, Turkissa, 10.–16.4.2014 (European Girls’ Mathematical Olympiad in Antalya, Turkey, 10–16 April, 2014, in Finnish), Solmu, 3/2014, 24–30.
  16. Zermelo ja aritmetiikan peruslause (Zermelo and the fundamental theorem of arithmetic, in Finnish), Solmu, 1/2014, 23–25.
  17. Kuusi haastavaa tehtävää: Euroopan tyttöjen matematiikkaolympialaiset Luxemburgissa 8.–14.4.2013 (Six challenging problems: The European Girls’ Mathematical Olympiad in Luxembourg in 8–14 April 2013, in Finnish), Solmu, 3/2013, 13–17.


  1. On Non-Scattering Energies, doctoral thesis, University of Helsinki, summer 2014.
  2. Eigenvalues of Periodic Magnetic Schrödinger Operators, licentiate’s thesis, University of Helsinki, fall 2011.
  3. The Fourier-Analytic Approach to Szemerédi’s Theorem, master’s thesis, University of Helsinki, fall 2009.
  4. Waring–Hilbertin lause (The Waring–Hilbert Theorem, in Finnish), bachelor’s thesis, University of Helsinki, fall 2008.