Ramūnas Garunkštis Professor at the Department of Probability Theory and Number Theory Faculty of Mathematics and Informatics Vilnius University Naugarduko 24, 03225 Vilnius, Lithuania
Research interests: Analytic Number Theory, Zeta Functions

### Papers

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 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 periodic zeta-function, Šiauliai Mathematical Seminar, 8(16) (2013), 49-62. (with R. Tamošiūnas). PDF
43. 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
44. 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
45. 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
46. Universality of the Selberg zeta-function for the modular group, Forum Mathematicum 25(3) (2013), 533-564, (with P. Drungilas and A. Kačėnas). PDF
47. On the roots of the equation $\zeta(s)=a$, Abh. Math. Semin. Univ. Hambg. 84 (2014), 1-15, (with J. Steuding). arXiv:1011.5339
48. Self-approximation of Hurwitz zeta-functions, Functiones et Approximatio 51(1) (2014), 181-188, (with E. Karikovas). PDF
49. 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
50. On the Speiser equivalent for the Riemann hypothesis, European Journal of Mathematics DOI 10.1007/s40879-014-0033-1, (with R. Šimėnas). 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.