Johannes Schoißengeier

• Phone: (+43-1) 4277-50686
• Fax: (+43-1) 4277-50620
• E-mail: hannes.schoissengeier@univie.ac.at
• Mailing address: Department of Mathematics, University of Vienna, Nordberstraße 15, A-1090 Wien, Austria

• 1973 Ph.D. University of Vienna,
  Thesis: Gleichmäßige Gleichverteilung in lokalkompakten Räumen (Well-distributed sequences in locally compact spaces)
• 1978 Habilitation University of Vienna,
  Thesis: Der Zusammenhang zwischen den Nullstellen der ζ-Funktion und Folgen der Form (g(p)) (mod 1), p prim (The connection between the zeros of the ζ-function and sequences of the shape (g(p)) (mod 1), p prime)

Scientific interests

• Uniform distribution
• Ostrowski exansions
• Functions of a real variable
• Analytic number theory
• Zeta functions
• Distribution of prime numbers
• Lattice points in convex domains
• Arithmetical functions
• Elementary number theory
• Algebraic number theory

Books

• with E. Hlawka, Zahlentheorie. Eine Einführung (Number Theory. An Introduction), Manz, Wien, 1979 (First edition), 1990 (Second edition). MR 82d:10001. Zbl. 412.10001.
• with E. Hlawka, R. Taschner, Geometrische und analytische Zahlentheorie (Geometric and Analytic Number Theory), Manz, Wien, 1986. MR 87h:11001. Zbl. 578.10001.
• with E. Hlawka, R. Taschner, Geometric and Analytic Number Theory, Springer, Berlin, etc., 1991. MR 92f:11002. Zbl. 749.11001.

Co-editor of:

• Proceedings of the Conference on Analytic and Elementary Number Theory, Vienna, July 18 - 20, 1996. Edited by W. G. Nowak and J. Schoißengeier Zbl. 868.00042.

Selected articles

• with W. Maxones, I. Richards, H. Rindler, Ein metrisches Ergebnis über die Diskrepanz von Folgen (A metric result on the discrepancy of sequences), Sitzungsber. Abt. II Österr. Akad. Wiss. Math.-Naturwiss. Kl. 185 (1976), 405-409. MR 58#22002. Zbl. 377.10026.
• with H. Niederreiter, Almost periodic functions and uniform distribution mod 1, J. Reine Angew. Math. 291 (1977), 189-203. MR 55#10412. Zbl. 338.10053.
• with H. Rindler, Gleichverteilte Folgen und differenzierbare Funktionen (Uniformly distributed sequences and differentiable functions), Monatsh. Math. 84 (1977), 125-131. MR 58#10801. Zbl. 371.10040.
• Über die Diskrepanz gewisser Folgen mod 1 mit Hilfe Diophantischer Approximation (On the discrepancy of certain sequences mod 1 with the help of Diophantine approximation), Math. Z. 159 (1978), 169-179. MR 58#10804. Zbl. 357.10027 and Zbl. 371.10041
• The connection between the zeros of the ζ-function and sequences (g(p)), p prime, mod 1. Monatsh. Math. 87 (1979), 21-52. MR 80g:10054. Zbl. 401.10046.
• On the discrepancy of sequences (αn^σ), Acta Math. Acad. Sci. Hung. 38 (1981), 29-43. MR 83i:10067. Zbl. 484.10032.
• Der numerische Wert gewisser Reihen (The numerical value of certain series), Manuscripta Math. 38 (1982), 257-263. MR 83i:10039. Zbl. 499.10013.
• On the discrepancy of (nα), Acta Arith. 44 (1984), 241-279. MR 86c:11056. Zbl. 506.10031 and Zbl. 544.10035.
• On the discrepancy of (nα) II, J. Number Theory 24 (1986), 54-64. MR 88d:11074. Zbl. 588.10058.
• Abschätzungen für ∑_n≤NB₁(nα) (Estimates for ∑_n≤NB₁(nα)), Monatsh. Math. 102 (1986), 59-77. MR 87j:11020. Zbl. 613.10011.
• An asymptotic expansion for ∑_n≤N{nα+β}, in: E. Hlawka, R. F. Tichy (Eds.), Number-Theoretic Analysis, Lecture Notes in Mathematics 1452, Springer, Berlin, etc., 1990, pp. 199-205. MR 92d:11077. Zbl. 722.11035.
• Change of variables in a multiple integral for local fields, Monatsh. Math. 114 (1992), 139-147. MR 94b:12003. Zbl. 764.12004.
• On the longest gaps in the sequence (nα) mod 1, Grazer Math. Ber. 318 (1993), 155-166. MR 94g:11056. Zbl. 792.11023.
• The discrepancy of (nα)_n≥1, Math. Ann. 296 (1993), 529-545. MR 94e:11086. Zbl. 786.11043.
• with C. Baxa, Minimum and maximum order of magnitude of the discrepancy of (nα), Acta Arith. 68 (1994), 281-290. MR 95j:11073. Zbl. 828.11038.
• with M. Kühleitner, W. G. Nowak, T. D. Wooley, On sums of two cubes: An Ω₊-estimate for the error term, Acta Arith. 85 (1998), 179-195. MR 99g:11119. Zbl. 916.11052.
• with C. Baxa, On the discrepancy of the sequence (α√n), J. Lond. Math. Soc. 57 (1998), 529-544. MR 99k:11118. Zbl. 938.11041.
• Another proof of a theorem by J. Beck, Monatsh. Math. 129 (2000), 147-151. MR 2001a:11120. Zbl. 991.11041.
• with G. Kuba, H. Müller, W. G. Nowak, Zur Verteilung der Potenzen ganzer Zahlen eines komplexen kubischen Zahlkörper (On the distribution of the powers of algebraic integers of a complex cubic number field), Abh. Math. Semin. Univ. Hamburg 70 (2000), 341-354. MR 2002f:11169. Zbl. 1008.11039.
• The integral mean of the discrepancy of the sequence (nα), Monatsh. Math. 131 (2000), 227-234. MR 2001h:11098. Zbl. 972.11067.
• with C. Baxa, Calculation of improper integral using (nα) - sequences, Monatsh. Math. 135 (2002), 265-277. MR 2003h:11084. Zbl. 1009.11054.
• with M. Drmota, Digital expansions with respect to different bases, Monatsh. Math. 138 (2003), 31-59. MR 2003m:11118.
• with H. Dirnböck, Curves related to triangles: The Balaton-Curves, J. Geom. Graph. 7 (2003), 23-39. MR 2004i:51013.
• with W. G. Nowak, The distribution of powers of integers in algebraic number fields, J. Théor. Nombres Bordeaux 16 (2004), 197-214.
• with K. Girstmair, On the arithmetic mean of Dedekind sums, Acta Arith. 116 (2005), 189-198. MR 2005h:11086.
• with L. Roçadas, An explicit formula for the L₂-discrepancy of (nα)-sequences, Computing 77 (2006), 113-128.