Lithuanian

Ramūnas Garunkštis

Professor at the
Department of Probability Theory and Number Theory
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

Papers

  1. On the Lerch zeta-function, Lith. Math. J. 36 (1996), 337-346.
  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 zeros of the derivative of the Lerch zeta-function, Liet. Matem. Rink. 42 (Special Issue) (2002), 47-49 (Lithuanian).
  13. On the zero distributions of Lerch zeta-functions, Analysis 22 (2002), 1-12 (with J. Steuding). PDF
  14. On a positivity property of the Riemann $\xi$-function, Liet. matem. rink. 42 (2002), 179-184. PDF
  15. On the universality of Estermann zeta-functions, Analysis 22 (2002), 285-296 (with A. Laurinčikas, R. Šleževičienė and J. Steuding). PDF
  16. On some inequalities concerning $\pi (x)$, Exp. Math. 11 (2002), 297-301. PDF
  17. The Lerch zeta-function, Kluwer Academic Publishers, 2002, 197 pp. (with A.Laurinčikas).
  18. 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
  19. On the mean square of Lerch zeta-functions, Arch. Math. 80 (2003), 47-60 (with A. Laurinčikas and J. Steuding). PDF
  20. On the Chebyshev function $\psi(x)$, Liet. matem. rink. 43 (2003), 487-496 = Lith. Math. J. 401-409.
  21. 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
  22. An approximation of the Hurwitz zeta-function by a finite sum, Liet. Matem. Rink. 43 (Special Issue) (2003), 32-34 (Lithuanian).
  23. 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
  24. An approximate functional equation for the Lerch zeta-function, Math. Notes 74 (2003), 469-476 (with A. Laurinčikas and J.Steuding). PDF
  25. Approximation of the Lerch zeta-function, Liet. matem. rink. 44 (2004), 176-180 = Lith. Math. J. 140-144. PDF
  26. Universality of Dirichlet L-functions with shifted characters, Liet. Matem. Rink. 44 (Special Issue) (2004), 48-50.
  27. Growth of the Lerch zeta-function, Liet. matem. rink. 45 (2005), 45-56 = Lith. Math. J. 34-43. PDF
  28. 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
  29. Simple zeros and discrete moments of the derivative of the Riemann zeta-function, J. Number Theory 115 (2005), 310-321 (with J. Steuding). PDF
  30. On the distribution of zeros of the Hurwitz zeta-function, Math. Comp. 76 (2007), 323-337 (with J. Steuding). PDF
  31. On the Backlund equivalent for the Lindelof hypothesis, Adv. Stud. Pure Math. 49 (2007), 91-104. PDF
  32. 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
  33. 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
  34. 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
  35. 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
  36. 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
  37. Self-approximation of Dirichlet L-functions, J. Number Theory, 131(7) (2011), 1286-1295. arXiv:1006.1507
  38. 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
  39. Uniqueness theorems for L-functions, Comment. Math. Univ. St. Pauli, 60, No. 1,2 (2011), 15-35. (with J. Grahl and J. Steuding). PDF
  40. Zeros of the Lerch transcendent function, Mathematical Modelling and Analysis, 17, No. 2 (2012), 245-250. (with A. Grigutis). PDF
  41. The a-values of the Selberg zeta-function, Lith. Math. J., 52, No. 2 (2012), 145-154. (with R. Šimenas). PDF
  42. Zeros of the Estermann zeta-function, Journal of the Australian Mathematical Society, Available on CJO 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. doi:10.1112/S146115701300003X (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).
  45. Universality of the Selberg zeta-function for the modular group, Forum Mathematicum, 25(3) (2013), 533-564, DOI: 10.1515/FORM.2011.127 (with P. Drungilas and A. Kačėnas). PDF

International conferences, visits

  1. The II International Conference “Analytic and Probabilistic Methods in Number Theory”, Palanga, Lithuania, September 23-27, 1996.
  2. Renyi Institute, Budapest, Hungary, November 1-30, 1997.
  3. 22nd European Meeting of Statisticians, 7th Vilnius Conf. on Probability Theory and Mathematical Statistics, Vilnius, Lithuania, August 12-18, 1998.
  4. Paul Erdos and his Mathematics, Budapest, Hungary, July 4-11, 1999.
  5. J.W. Goethe University, Frankfurt on Main, Germany, November 2-30, 1999.
  6. Colloquium on Number Theory in honour of the 60th birthday of Professors K. Gyory and A. Sarkozy, Debrecen, Hungary, July 3-7, 2000.
  7. IV International Conference “Modern Problems of Number Theory and Its Applications” dedicated to 180th anniversary of P.L. Chebysheff and 110th anniversary of I.M. Vinogradov, Tula, Russia, September 10-15, 2001.
  8. The III International Conference “Analytic and Probabilistic Methods in Number Theory”, Palanga, Lithuania, September 24-28, 2001.
  9. J.W. Goethe University, Frankfurt on Main, Germany, June 5-July 5, 2002.
  10. Freiburg University, Germany, June 7, 2002.
  11. Workshop “Special Activity in Analytic Number Theory and Diophantine equations”, Max Planck Institute for Mathematics, Bonn, Germany, June 24-28, 2002.
  12. Voronoi conference on analytic number theory and spatial tessellations, Kyiv, Ukraine, September 22-28, 2003.
  13. J.W. Goethe University, Frankfurt on Main, Germany, January 27-February 26, 2004.
  14. Nagoya University, Nagoya, Japan, June 11-19, 2005.
  15. International Conference on Probability and Number Theory (P&NT 05), Kanazawa, Japan, June 20-24, 2005.
  16. The 17-th Czech and Slovak International Conference on Number Theory, Malenovice, Czech Republic, September 5-10, 2005.
  17. The 30th birthday of Voronin's universality theorem. Colloquium: value distribution of Dirichlet series, Madrid, Spain, December 5-9, 2005.
  18. Conference “Advances in Number Theory and Random Matrix Theory”, University of Rochester, Rochester, NY, USA, , June 5-8, 2006.
  19. The IV International Conference “Analytic and Probabilistic Methods in Number Theory”, Palanga, Lithuania, September 24-30, 2006.
  20. “West Coast Number Theory Conference”, Ensenada, Baja California, Mexico, December 17-21, 2006.
  21. “International Conference on Number Theory” dedicated to the 60th birthday of Professor Antanas Laurinčikas, Šiauliai, Lithuania, August 11-15, 2008.
  22. “New Directions in the Theory of Universal Zeta- and L-Functions”, Würzburg, Germany, October 6-10, 2008.
  23. Würzburg University, Würzburg, Germany, December 9-20, 2009.
  24. “15th International Conference Mathematical Modelling and Analysis”, Druskininkai, Lithuania, May 26-29, 2010.
  25. Satellite Conference to ICM 2010 “Analytic and Combinatorial Number Theory”, Institute of Mathematical Sciences, Chennai, India, August 29-September 3, 2010.
  26. Conference “Functions in Number Theory and Their Probabilistic Aspects”, RIMS, Kyoto University Kyoto, Japan, December 13-17, 2010.
  27. “Workshop on various zeta functions and related topics”, The University of Tokyo, Tokyo, Japan, December 21 and 22, 2010.
  28. “27th Journées Arithmétiques”, Vilnius University, Vilnius, Lithuania, 27th June - 1st July 2011.
  29. The V International Conference “Analytic and Probabilistic Methods in Number Theory”, Palanga, Lithuania, September 4-10, 2011.
  30. Würzburg University, Würzburg, Germany, October 1-30, 2011.
  31. Conference “Synergies And Vistas in Analytic Number Theory”, University of Oxford, Oxford, UK, September 3-7, 2012.