Ramūnas Garunkštis

Professor at the
Institute of Mathematics
Faculty of Mathematics and Informatics
Vilnius University
Naugarduko 24, 03225 Vilnius, Lithuania

E-mail: ramunas dot garunkstis at mif dot vu dot lt

Research interests: Analytic Number Theory, Zeta Functions


  1. On the Lerch zeta-function, Lith. Math. J. 36 (1996), 337-346 (with A. Laurinčikas).
  2. The universality theorem with weight for the Lerch zeta-function, in: New Trends in Probability and Statistics. V.4: Analytic and Probabilistic Methods in Number Theory, Proceedings of the Second Intern. Conf. in Honour of J. Kubilius, Palanga, Lithuania, 23-27 September 1996. Eds. A.Laurinčikas, E.Manstavičius and V.Stakenas, Vilnius: TEV, Utrecht: VSP, (1997), 59-67.
  3. An explicit form of the limit distribution with weight for the Lerch zeta-function in the space of analytic functions, Lith. Math. J. 37 (1997), 230-242.
  4. On one Hilbert's problem for the Lerch zeta-function, Publ. Inst. Math., 65 (79) (1999), 63-69 (with A. Laurinčikas).
  5. On zeros of the Lerch zeta-function, in: Number Theory and Its Applications, S.Kanemitsu and K.Gyory (eds.), Kluwer Academic Publishers, (1999), 129-143 (with A. Laurinčikas). PDF
  6. On zeros of the Lerch zeta-function.II, in: Probability Theory and Mathematical Statistics, Proceedings of the Seventh Vilnius Conf. 1998, B.Grigelionis et al. (Eds.), TEV/Vilnius, VSP/Utrecht, (1999), 267-276. PDF
  7. On zeros of the Lerch zeta function. III, Scient. works of Lith. Math. Soc.: supl. to "Liet. Matem. Rink.", Vilnius: Technika, 1999, pp. 24-30. PDF
  8. A note on the Riemann $\xi$-function, Liet. Matem. Rink., 40 (Special Issue) (2000), 18-20 (Lithuanian).
  9. The Lerch zeta-function, Integral Transforms and Special Functions, 10 (2000), 211-226 (with A. Laurinčikas).
  10. A note on the zeros of the Lerch zeta-function, Liet. Matem. Rink. 41 (Special Issue) (2001), 53-57 (Lithuanian).
  11. Twists of Lerch zeta-functions, Liet. matem. rink. 41 (2001), 172-182 (with J. Steuding). PDF
  12. On the zero distributions of Lerch zeta-functions, Analysis 22 (2002), 1-12 (with J. Steuding). PDF
  13. On a positivity property of the Riemann $\xi$-function, Liet. matem. rink. 42 (2002), 179-184. PDF
  14. On the universality of Estermann zeta-functions, Analysis 22 (2002), 285-296 (with A. Laurinčikas, R. Šleževičienė and J. Steuding). PDF
  15. On some inequalities concerning $\pi (x)$, Exp. Math. 11 (2002), 297-301. PDF
  16. The Lerch zeta-function, Kluwer Academic Publishers, 2002, 197 pp. (with A.Laurinčikas).
  17. Do Lerch zeta-functions satisfy the Lindelof hypothesis?, in: Analytic and Probabilistic Methods in Number Theory, Proceedings of the Third Intern. Conf. in Honour of J. Kubilius, Palanga, Lithuania, 24-28 September 2001, (eds. A. Dubickas, A. Laurinčikas and E. Manstavičius), TEV, Vilnius, (2002), 61-74 (with J. Steuding). PDF
  18. On the mean square of Lerch zeta-functions, Arch. Math. 80 (2003), 47-60 (with A. Laurinčikas and J. Steuding). PDF
  19. On the Chebyshev function $\psi(x)$, Liet. matem. rink. 43 (2003), 487-496 = Lith. Math. J. 401-409.
  20. The effective universality theorem for the Riemann zeta function, in: Proceedings of the session in analytic number theory and Diophantine equations, MPI-Bonn, January - June 2002, Ed. by D. R. Heath-Brown, B. Z. Moroz, Bonner mathematische Schriften, 360 (2003), 21 pp. PDF
  21. An approximation of the Hurwitz zeta-function by a finite sum, Liet. Matem. Rink. 43 (Special Issue) (2003), 32-34 (Lithuanian).
  22. On the Voronin's universality theorem for the Riemann zeta-function, Proceedings of Scientific Seminar of the Faculty of Physics and Mathematics, Šiauliai University 6 (2003), 29-33. PDF
  23. An approximate functional equation for the Lerch zeta-function, Math. Notes 74 (2003), 469-476 (with A. Laurinčikas and J.Steuding). PDF
  24. Approximation of the Lerch zeta-function, Liet. matem. rink. 44 (2004), 176-180 = Lith. Math. J. 140-144. PDF
  25. Universality of Dirichlet L-functions with shifted characters, Liet. Matem. Rink. 44 (Special Issue) (2004), 48-50.
  26. Growth of the Lerch zeta-function, Liet. matem. rink. 45 (2005), 45-56 = Lith. Math. J. 34-43. PDF
  27. Note on the zeros of the Hurwitz zeta-function, in: Voronoi's impact on modern science. Book 3: proceedings of the third Voronoi Conference on Number Theory and Spatial Tessellations. Mathematics and its Applications, 55 (2005), 10-12. PDF
  28. Simple zeros and discrete moments of the derivative of the Riemann zeta-function, J. Number Theory 115 (2005), 310-321 (with J. Steuding). PDF
  29. On the distribution of zeros of the Hurwitz zeta-function, Math. Comp. 76 (2007), 323-337 (with J. Steuding). PDF
  30. On the Backlund equivalent for the Lindelof hypothesis, Adv. Stud. Pure Math. 49 (2007), 91-104. PDF
  31. Sum of the periodic zeta-function over the nontrivial zeros of the Riemann zeta-function, Analysis, München, 28 (2008), 209-217 (with J. Kalpokas). PDF
  32. Note on zeros of the derivative of the Selberg zeta-function, Arch. Math. 91 (2008), 238-246. PDF . Corrigendum, Arch. Math. 93 (2009), page 143. PDF
  33. Selberg's Central Limit Theorem on the Critical Line and the Lerch Zeta-Function, in: Proceedings of the conference "New Directions in the Theory of Universal Zeta- and L-Functions", Würzburg, Germany, October 6-10, 2008, Shaker Verlag, (2009), 57-64 (with A. Grigutis and A. Laurinčikas). PDF
  34. Effective uniform approximation by the Riemann zeta-function, Publ. Mat. 54 (2010), 209-219 (with A. Laurinčikas, K. Matsumoto, J. Steuding and R. Steuding). PDF
  35. Sum of the Dirichlet L-function over nontrivial zeros of another Dirichlet L-function, Acta Math. Hungar., 128 (2010), 287-298 (with J. Kalpokas and J. Steuding). PDF
  36. Self-approximation of Dirichlet L-functions, J. Number Theory, 131(7) (2011), 1286-1295. arXiv:1006.1507
  37. Questions around the nontrivial zeros of the Riemann zeta-function - computations and classifications, Math. Model. Anal., 16(1) (2011), 72-81. (with J. Steuding). PDF
  38. Uniqueness theorems for L-functions, Comment. Math. Univ. St. Pauli, 60, No. 1,2 (2011), 15-35. (with J. Grahl and J. Steuding). PDF
  39. Zeros of the Lerch transcendent function, Mathematical Modelling and Analysis, 17, No. 2 (2012), 245-250. (with A. Grigutis). PDF
  40. The a-values of the Selberg zeta-function, Lith. Math. J., 52, No. 2 (2012), 145-154. (with R. Šimenas). PDF
  41. Zeros of the periodic zeta-function, Šiauliai Mathematical Seminar, 8(16) (2013), 49-62. (with R. Tamošiūnas). PDF
  42. Zeros of the Estermann zeta-function, Journal of the Australian Mathematical Society 94 (2013), 38-49, doi:10.1017/S1446788712000419 (with A. Dubickas, J. Steuding, and R. Steuding). PDF
  43. Complex B-splines and Hurwitz zeta functions, LMS Journal of Computation and Mathematics 16 (2013), 61-77, (with B. Forster, P. Massopust, and J. Steuding). PDF
  44. The discrete mean square of the Dirichlet L-function at nontrivial zeros of another Dirichlet L-function, International Journal of Number Theory 9(4) (2013), 945-963, (with J. Kalpokas). PDF
  45. Universality of the Selberg zeta-function for the modular group, Forum Mathematicum 25(3) (2013), 533-564, (with P. Drungilas and A. Kačėnas). PDF
  46. On the roots of the equation $\zeta(s)=a$, Abh. Math. Semin. Univ. Hambg. 84 (2014), 1-15, (with J. Steuding). arXiv:1011.5339
  47. Self-approximation of Hurwitz zeta-functions, Functiones et Approximatio 51(1) (2014), 181-188, (with E. Karikovas). PDF
  48. The a-points of the Selberg zeta-function are uniformly distributed modulo one, Illinois J. Math. 58(1) (2014), 207–218, (with J. Steuding and R. Šimėnas). PDF
  49. On the Speiser equivalent for the Riemann hypothesis, European Journal of Mathematics 1 (2015), 337-350, (with R. Šimėnas). PDF
  50. The size of the Selberg zeta-function at places symmetric with respect to the line Re(s)= 1/2, Results. Math. 70(1) (2016), 271–281, (with A. Grigutis). PDF
  51. Sum of the Lerch zeta-function over nontrivial zeros of the Dirichlet L-function, From arithmetic to zeta-functions. Number theory in memory of Wolfgang Schwarz. Cham: Springer. (2016), 141–153, (with J. Kalpokas). PDF
  52. On the distribution of the a-values of the Selberg zeta-function associated to finite volume Riemann surfaces, J. Number Theory 173 (2017), 64–86, (with R. Šimėnas). PDF
  53. Zeros of the Riemann zeta-function and its universality, Acta Arith. 181(2) (2017), 127-142 (with A. Laurinčikas and R. Macaitienė).
  54. Symmetry of zeros of Lerch zeta-function for equal parameters, Lith. Math. J. 57(4) (2017), 433-440 (with R. Tamošiūnas). PDF
  55. Discrete mean square of the Riemann zeta-function over imaginary parts of its zeros, Period. Math. Hungar. 76 (2018), 217-228 (with A. Laurinčikas). arXiv:1608.08493
  56. The Riemann hypothesis and universality of the Riemann zeta-function, Math. Slovaca 68(4) (2018), 741-748 (with A. Laurinčikas). PDF
  57. Growth of the Selberg zeta-function, Kyushu J. Math. 72 (2018), 441-447. PDF
  58. Zero-free regions for derivatives of the Selberg zeta-function, Publ. Math. Debrecen 93 (2018), 369-385. PDF
  59. Asymptotic distribution of Beurling integers, Int. J. Number Theory 14(10) (2018), 2555-2569 (with L. Kaziulytė). PDF
  60. The size of the Lerch zeta-function at places symmetric with respect to the line Re(s)=1/2, Czechoslovak Math. J., 69 (2019), 25-37 (with A. Grigutis). PDF
  61. On the vertical distribution of the a-points of the Selberg zeta-function attached to a finite volume Riemann surface, Lith. Math. J., 59 (2019), 143-155 (with R. Šimėnas). PDF
  62. Second moment of the Beurling zeta-function, Lith. Math. J., 59 (2019), 317-337 (with P. Drungilas and A. Novikas). PDF
  63. Zeros of the extended Selberg class zeta-functions and of their derivatives, Turkish Journal of Mathematics., 43 (2019), 2921-2930 arXiv:1904.03123
  64. Zeros of the Lerch zeta-function and of its derivative for equal parameters, to appear in Bull. Math. Soc. Sci. Math. Roumanie (with R. Tamošiūnas). arXiv:1902.03064
  65. On primeness of the Selberg zeta-function, to appear in Hokkaido Math. J. (with J. Steuding). arXiv:1908.03108