Preprints



Papers


73. Benjamini-Schramm convergence and zeta functions. 
Res. Math. Sci. 7 (2020), no. 3, Paper No. 27 article preprint

72. Building lattices and zeta functions. (with Ming-Hsuan Kang and Rupert McCallum)
Adv. in Geom. 20, no. 2, 249 - 272  (2020) article preprint

71. A prime geodesic theorem for SL3(Z). (with Yasuro Gon and Polyxeni Spilioti)
Forum Math. 31, No. 5, 1179--1201 (2019) article preprint

70. Spectral theory for non-unitary twists.
Hiroshima Math. J. 49, No. 2, 235--249 (2019) article preprint

69. Benjamini-Schramm and spectral convergence.
L'Enseignement Mathématique (2) 64, No 3-4, 371--394 (2018) article preprint

68. Tree-lattice zeta functions and class numbers. (with Ming-Hsuan Kang)
Michigan Math. J. 67,  617-645 (2018) article preprint

67. On Haar systems for groupoids.
Z. Anal. Anwend. 37,  3, 269–275 (2018) article preprint

66. A prime geodesic theorem for higher rank buildings. (with Rupert McCallum)
Kodai Math. J. 41, 444-455 (2018) article preprint

65. Eisenstein series with non-unitary twists. (with Frank Monheim)
J. Korean Math. Soc. 55, No. 3. 507-530 (2018) article preprint

64. Closed geodesics and bounded gaps.
Math. Z. 287(1), 547-554 (2017). article preprint

63. Belian categories.
Absolute arithmetic and F1-geometry, 39-80,  Eur. Math. Soc., Zürich, 2016. book

62. A trace formula for non-unitary representations of a uniform lattice. (with Frank Monheim)
Math. Z. 284(3), 1199-1210 (2016). article preprint

61. Zeta functions of F1-buildings. (with Ming-Hsuan Kang)
J. Math. Soc. Japan. Volume 68, Number 2, 807-822 (2016). article preprint

60. Trace class groups. (with Gerrit van Dijk)
Journal of Lie Theory 26, No. 1, 269-291 (2016). article preprint

59. Ihara zeta functions of infinite weighted graphs.
SIAM J. discrete Math. Vol. 29, No. 4, 2100-2116 (2015). article preprint

58. Two application of nets. (with Ralf Beckmann)
Ann. Funct. Anal. 6. no. 3, 176-190 (2015). article preprint

57. Counting and zeta functions over F1. (with Shin-Ya Koyama and Nobushige Kurokawa)
Abh. Math. Sem. Hamburg. Vol. 85, Issue 1, 59-71 (2015). article preprint

56. Geometric zeta functions for higher rank p-adic groups. (with Ming-Hsuan Kang)
Illinois J. Math. Vol. 58, Issue , 719-738 (2014). article preprint

55. Ihara zeta functions and class numbers.
Adv. Studies in Contemp. Math. Vol. 24, Issue 4, 439-450 (2014). preprint

54. Fourier expansion along geodesics on Riemann surfaces.
Central European Journal of Mathematics 12, No 4, 559-573 (2014). article preprint

53. Congruence schemes.
International Journal of Math. Vol. 24, Issue 2 [46 pages] (2013). article preprint

52. Iterated Integrals and higher order invariants. (with Ivan Horozov)
Can. J. Math. 65, 544-552 (2013). article preprint

51. Belian categories.
Far East J. Math. Sci. 70, Issue 1, 1-46 (2012). article preprint

50. Invariants, cohomology, and automorphic forms of higher order.
Selecta Math. New Ser. 18, No 4, 855-883 (2012). article preprint

49. Holomorphic torsion and closed geodesics.
J. Fixed Point Theory Appl. 9, 25-53 (2011). article preprint

48. Lewis-Zagier Correspondence for higher order forms.
Pacific Journal of Mathematics 249.1, 11-21 (2011). article preprint

47. Higher order invariants in the case of compact quotients.
Central European Journal of Mathematics 9.1, 85-101 (2011). article preprint

46. A new multiple Dirichlet series induced by a higher order form. (with Nikolaos Diamantis)
Acta Arithmetica 142.4, 303-309 (2010). article preprint

45. Higher order group cohomology and the Eichler-Shimura map.
J. reine u. angew. Math. 629, 221-235 (2009). article preprint

44. Automorphic forms of higher order. (with Nikolaos Diamantis)
Journal of the London Mathematical Society. 80, 18-34 (2009). article preprint

43. A prime geodesic theorem for higher rank II: singular geodesics.
Rocky Mountain J. Math. 39, No. 2, 485-507 (2009). article preprint

42. F1-schemes and toric varieties.
Contributions to Algebra and Geometry Vol. 49, No. 2, pp. 517-525 (2008). article preprint

41. Absolute zeta functions. (with S. Koyama and N. Kurokawa)
Proc. Japan Acad. Ser. A Math. Sci. 84, no. 8, 138-142 (2008). article

40. A prime geodesic theorem for SL(4). (with Mark Pavey)
Ann. Global Anal. Geom. 33, No. 2, 161-205 (2008). article

39. A Lewis Correspondence for submodular groups. (with J. Hilgert)
Forum Math. 19, no. 6, 1075-1099 (2007). article preprint

38. Lefschetz formulae for p-adic groups.
Chinese Ann. Math. Ser. B. 28, no. 4, 463-474 (2007). article preprint

37. A higher rank Lefschetz formula.
J. Fixed Point Theory Appl. 2, 1-40 (2007). article preprint erratum

36. Class numbers of orders in complex quartic fields. (with Mark Pavey)
Math. Ann. 338, no. 3, 767-799 (2007). article preprint

35. Generalised Selberg zeta functions and a conjectural Lefschetz formula.
Proceedings of Symp. in Pure Math. 75, 177- 190 (2006). book preprint

34. Remarks on zeta functions and K-theory over F1.
Proc. Japan Acad. Ser. A Math. Sci. 82 no 8, 141-146 (2006). article

33. Invariant triple products.
Int. J. Math. Sci., Art. ID 48274, 22 pp. (2006). article

32. A discrete Lefschetz formula.
Topology Appl., Volume 153, Issue 14 , 2363-2381 (2006). article preprint

31. The Ihara-Selberg zeta function for PGL(3) and Hecke operators. (with J. W. Hoffman)
Internat. J. Math., Vol. 17, No. 2, 143-156 (2006). article preprint

30. Asymptotics of class numbers. (with W. Hoffmann)
Invent. Math. 160, 647 - 675 (2005). article

29. Schemes over F1.
Progress in Mathematics, Vol. 239 Geer, Moonen, Schoof (Eds.) Birkäuser 2005, 87-100. article preprint

28. Cohomology of arithmetic groups with infinite dimensional coefficient spaces. (with J. Hilgert)
Doc. Math. 10, 199-216 (2005). article erratum

27. A prime geodesic theorem for higher rank spaces.
Geometric and Functional Analysis 14, 6, 1238-1266 (2004). article preprint

26. Panorama of zeta functions.
in: Erich Kähler: Mathematical Works. de Gruyter 2003. book preprint

25. A dynamical Lefschetz trace formula for algebraic Anosov diffeomorphisms. (with C. Deninger)
Abh. Math. Sem. Hmbg. 73, 81-98 (2003). journal preprint

24. Mellin transforms of p-adic Whittaker functions.
Math. Nachr. 261-262, 37-46 (2003). article preprint

23. Lefschetz formulae and zeta functions.
Journal of the Ramanujan Mathematical Society 18, 139-152 (2003). journal preprint

22. Mellin transforms of Whittaker functions.
Can. Math. Bull. Vol. 45 (3), 364-377, (2002). article preprint

21. Class numbers of orders in cubic fields.
J. Number Theory 95, 150-166 (2002). article preprint

20. A Polya-Hilbert operator for automorphic L-functions.
Indag. Mathem. 12(2), 157-175 (2001). article preprint

19. Harmonic Analysis on the quotient Q* x Q \ A* x A.
Acta Mathematica Scientia 21, 21-28 (2001). journal preprint

18. Geometric zeta-functions of locally symmetric spaces.
American Journal of Mathematics. 122, vol 5, 887-926 (2000). article preprint

17. Differential operators on equivariant vector bundles over symmetric spaces.
Electron. J. Diff. Eqns., Vol. 2000, No. 59, pp. 1-8 (2000). article

16. Combinatorial L^2-determinants.
Proc. Edinburgh Math. Soc. 43, 185-194 (2000). journal preprint

15. On limit multiplicities of automorphic forms. (with Werner Hoffmann)
Can. J. Math. 51, 952-976 (1999). article

14. Spectral estimates for towers of noncompact quotients. (with Werner Hoffmann)
Can. J. Math. 51, 266-293 (1999). article

13. Equivariant torsion of locally symmetric spaces.
Pac. J. Math. 182, 205-227 (1998). article

12. Geometric zeta-functions on p-adic groups.
Math. Japon. 47, No. 1, 1-17 (1998). (awarded the JAMS-Prize 1998). journal preprint

11. Regularized and L2-determinants.
Proc. of the London Math. Soc. 76, 150-174 (1998). article preprint

10. On the index of Dirac operators on arithmetic quotients.
Bull. Australian Math. Soc. 56, 489-497 (1997). journal preprint

9. A Lefschetz formula for flows.
Math. Res. Letters 4, 513-520 (1997). article

8. A determinant formula for the generalized Selberg zeta function.
Quarterly J. Math. 47, 435-453 (1996). article

7. Torus actions on compact quotients.
J. of Lie Theory 6, 179-190 (1996). article

6. Product expansions for zeta functions attached to locally symmetric spaces of higher rank.
Duke Math. J. 82, 71-90 (1996). article

5. Higher torsion zeta functions.
Adv. Math. 110, 109-128 (1995). article

4. Invariant Differential operators are linear combinations of symmetric positive ones.
Math. Ann. 297, 535-538 (1993). article

3. Theta correspondences for Eisenstein series. (with Aloys Krieg)
Math. Z. 208, 273-288 (1991). article

2. Invariant operators on higher K-types..
J. reine u. angew. Math. 412, 97-107 (1990). article

1. The Selberg trace formula and the of Ruelle zeta function for compact hyperbolics.
Abh. Hamb. Math. Sem. 59, 101-106 (1989). article