The Number Theory Group at "Universität für Bodenkultur" in Vienna

(“BOKU – University of Natural Resources and Applied Life Sciences, Vienna”)

 

Historical remarks: At "Universität für Bodenkultur" in Vienna, analytic number theory has a remarkable tradition. In fact, since the early 1960's the mathematics chair was held by Karl Prachar whose contributions to the theory of primes (in particular his monograph Primzahlverteilung) obtained the highest esteem by mathematicians all over the world. After his retirement in 1992, a fortunate decision of the hiring committee made possible a successful continuation of this number theoretic tradition.


Nowadays, there is a small but efficient group working on topics like the theory of lattice points in large regions, the asymptotic behaviour of arithmetic functions, estimations of exponential sums, uniform distribution of sequences, Diophantine approximation, etc.: 

  • Werner Georg Nowak, at present head of the Institute of Mathematics, received his Ph.D. (1979) and his "Habilitation" (1983) from the University of Vienna, for work on generalizations on the Gauss circle problem, carried out under the supervision of Edmund Hlawka. His research concentrates on the theory of lattice points in large regions and on the asymptotic theory of arithmetic functions.


List of all publications

Recent Publications: 

    • Divisor problems in special sets of positive integers, AMUC 61 (1992), 101-115.
      (This item has been stored at the journal's WWW-server. If interested click on here). 
    • On the value distribution of a class of arithmetic functions, Comment.Math.Univ.Carolinæ 37 (1996), 117-134. 
    • Primitive lattice points in starlike planar sets, Pacific J. 179 (1997), 163-178.


(Stored at the journal's WWW-server. If interested click on here.) 

    • Primitive lattice points in convex planar domains, Acta Arithmetica 76 (1996), 271-283. (Joint work with Martin Huxley.) 
    • On sums and differences of two relative prime cubes, II. Proceedings of the Czech and Slovake Number Theory Conference 1995, Tatra Mountains Publications 11 (1997), 23-34. 
    • Fractional part sums and lattice points. Proc. Edinburgh Math. Soc. 41 (1998), 497-515. 
    • On sums of two cubes: An Omega-plus-estimate for the error term. (Joint work with Manfred Kühleitner, Johannes Schoißengeier and Trevor Wooley.) Acta Arithmetica 85 (1998), 179-195. 
    • On differences of two k-th powers of integers. Ramanujan J. 2 (1998), 421-440. 
    • The asymptotic behaviour of the mean-square of fractional part sums (with M. Kühleitner). Proc. Edinburgh Math. Soc. 43 (2000), 309-323. 
    • The critical determinant of the double paraboloid and Diophantine approximation in R3 and R4. Math. Pannonica 10 (1999), 111-122.   (PDF-File)
    • Diophantine approximation in Rs: On a method of Mordell and Armitage. Proceedings of the Number Theory Conference held at Graz in September 1998, eds. F. Halter-Koch and R.F. Tichy, W. de Gruyter, Berlin - New York 2000, pp. 339-349.   (PDF-File)
    • Potenzen von Gaußschen ganzen Zahlen in Quadraten (with H. Müller). Mitt. Math. Ges. Hamburg 18 (1999), 119-126. 
    • On ternary cubic forms. Math. Pannonica 11 (2000), 87-100.   (PDF-File)
    • On sums of two k-th powers: a mean-square bound over short intervals. Funct. Approx. 28 (2000), 117-125.
    • Zur Verteilung der Potenzen ganzer Zahlen eines komplexen kubischen Zahlkörpers (with G. Kuba, H. Müller, J. Schoißengeier). Abh. Math. Sem. Hamburg 70 (2000), 341-354.
    • Primitive lattice points in a thin strip along the boundary of a convex planar domain (with E. Krätzel ). Acta Arithmetica 99 (2001), 331-341. 
    • On fractional part sums : A mean-square asymptotics over short intervals. Monatsh.f.Math.  137 (2002), 227 - 238. (PDF-File)
    • On the divisor problem: Moments of D(x) over short intervals. Acta Arithmetica 109 (2003), 329-341. (PDF-File)
    • The distribution of powers of integers in algebraic number fields (with J. Schoißengeier). J. Th. Nombres Bordeaux 16 (2004), 197-214.  (PDF-File)
    • Primitive lattice points inside an ellipse. To appear in Czech. J. Math. (PDF-File)
    • The average number of solutions of the Diophantine equation U² + V² = W³ and related arithmetic functions (with M. Kühleitner). Acta Math. Hungar.  104 (2004), 225-240. (PDF-File)
    • Lattice points in a circle: An improved mean-square asymptotics. Acta Arithm. 113 (2004), 259 – 272.
    • The Piltz divisor problem in number fields: An improved lower bound by Soundararajan’s method (with K. Girstmair, M. Kühleitner, W. Müller). Acta Arithm. 117 (2005), 187-206.


E-mail: nowak@mail.boku.ac.at

  • Gerald Kuba received his Ph.D. in 1991 for work on mean value theorems for certain arithmetic functions with W.G. Nowak as his advisor.


List of all publications

Recent Publications: 

o                     The number of lattice points above the catenary, Acta Math. Hungar. 87 (1-2)(2000), 173-178.
o                     On the distribution of squares of integral quaternions. Acta Arithmetica XCIII.4 (2000), 359-372.
o                     On the circle problem with gerneral weight. Math. Slovaca 51, No.1 (2001), 45-57.
o                     On rounding error sums related to the circle problem. Acta Math. Hungar. 92 (2001), 325-332.
o                     On the distribution of squares of hypercomplex integers. Journal of Number Theory 88 (2001), 313-334.
o                     On the distribution of squares of integral quaternions II. Acta Arithmetica 101.1 (2002), 81-95.
o                     On rounding error sums related to the circle problem II. Acta Math Hungar. 95 (2002), 115-124
o                     The true order of magnitude of Lamè rounding error sums. Arch.Math. 79 (2002), 534-542.
o                     Zur Verteilung der Quadrate ganzer Zahlen in rationalen Quaternionenalgebren. Abh. Math.Sem.Univ.Habmurg 72 (2003), 145-163.
o                     On the distribution of squares of integral Cayley numbers. Acta Arithmtica 108.3 (2003), 253-265.
o                     On the number of lattice points in certain planar segments. Math. Slovaca 53, No. 2 (2003), 173-187.
o                     Zerlegungen des Raumes in Translate einer Schraublinie. Mitt.Math.Ges.Hamburg 19 (2000), 149-153.


E-mail:  Kuba@edv1.boku.ac.at

 

  • Manfred Kühleitner received his Ph.D. in 1992 for work on lower and upper bounds on analytic number theoretic problems with W.G. Nowak as his advisor.


List of all publications

Recent Publications: 

    • Comparing the number of abelian groups and of semisimple rings of a given order, Math. Slovaca 45 (1995), 509-518. 
    • On the asymmetric divisor problem with congruence conditions, Comment. Mat. Univ. Carolinæ 37 (1996), 99-116. 
    • An Omega theorem on the general asymmetric divisor problem, J. Number Theory 65 (1997), 268-278. 
    • An Omega Theorem on differences of two squares, II. Acta Math. Univ. Comenianæ18 (1999), 27-35. 
    • On a generalization of a formula of Sierpinski. Math. Pannonica 9 (1998), 91-101. 
    • On a generalization of a formula of Sierpinski, II. Math. Pannonica 9 (1998), 267-279. 
    • On sums of two k-th powers: an asymptotic formula for the error term. Acta Arithmetica 92 (2000), 263-276. 
    • On differences of two k-th powers: an asymptotic formula for the error term. J. Number Th. 76 (1999), 22-44. 
    • Lattice points in bodies of revolution in R³. Arch. Math. (Basel) 74 (2000), 234-240. 
    • A remark on a theorem of Tsang: on lattice points in rational ellipsoids. Abh. Math. Sem. Univ. Hamburg, to appear. 
    • On the class number of binary quadratic forms: an Omega estimate for the error term. Preprint. 


E-mail:  kleitner@edv1.boku.ac.at

 

Link zum aktuellen Programm des BOKU-Seminars

 

Links to other number theory groups in Austria:

There are a lot of other people in Austria doing research in number theory.


Some of them have WWW-homepages: 

To the homepage of the Institute of Mathematics

W.G. Nowak, Institut für Mathematik    2004-03-01