- Maximal order of a class of multiplicative functions
- 'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function
- Generalised prime systems with periodic integer counting function
- Flows of Mellin transforms with periodic integrator
- Determinants of multiplicative Toeplitz matrices
- Asymptotic expansions for Taylor coefficients of the composition of two functions
- Omega-results for Beurling's zeta function and lower bounds for the generalised Dirichlet divisor problem
- A lower bound for the Lindelof function associated to generalised integers
- An arithmetical mapping and applications to Omega-results for the Riemann zeta function
- Orders of growth of real functions
Titus Hilberdink
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+44 (0) 118 378 5020
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Lecturer
Office
Room 307Building location
MathematicsAreas of interest
- Analytic number theory
- Tauberian theory
- Functional equations
Teaching
Research centres and groups
Websites/blogs
Recent papers
Publications
- Hilberdink, T. (2020) Asymptotics of entire functions and a problem of hayman. Quarterly Journal of Mathematics , 71 (2). pp. 667-676. ISSN: 0033-5606 | doi: https://dx.doi.org/10.1093/qmathj/haz061
- Al-Qabani, A. , Hilberdink, T. , Virtanen, J. (2020) Fredholm theory of Toeplitz operators on doubling Fock Hilbert spaces. Mathematica Scandinavica , 126 (3). pp. 593-602. ISSN: 1903-1807 | doi: https://dx.doi.org/10.7146/math.scand.a-120920
- Hilberdink, T. , Luca, F. , Toth, L. (2020) On certain sums concerning the gcd’s and lcm’s of k positive integers. International Journal of Number Theory , 16 (1). pp. 77-90. ISSN: 1793-7310 | doi: https://dx.doi.org/10.1142/S1793042120500049
- Neamah, A. and Hilberdink, T. (2019) The average order of the Möbius function for Beurling primes. International Journal of Number Theory , 16 (5). pp. 1005-1011. ISSN: 1793-7310 | doi: https://dx.doi.org/10.1142/s1793042120500517
- Hilberdink, T. (2019) Power moments and value distribution of functions. Transactions of the American Mathematical Society , 371 pp. 1-31. ISSN: 1088-6850 | doi: https://dx.doi.org/10.1090/tran/7581
- Hilberdink, T. (2018) Quasi Kronecker products and a determinant formula. Linear Algebra and its Applications , 87 (102). pp. 87-102. ISSN: 0024-3795 | doi: https://dx.doi.org/10.1016/j.laa.2017.09.011
- Hilberdink, T. (2017) Matrices with multiplicative entries are tensor products. Linear Algebra and its Applications , 532 pp. 179-197. ISSN: 0024-3795 | doi: https://dx.doi.org/10.1016/j.laa.2017.06.037
- Hilberdink, T. (2017) Singular values of multiplicative Toeplitz matrices. Linear and Multilinear Algebra , 65 (4). pp. 813-829. ISSN: 1563-5139 | doi: https://dx.doi.org/10.1080/03081087.2016.1204978
- Hilberdink, T. and Tóth, L. (2016) On the average value of the least common multiple of k positive integers. Journal of Number Theory , 169 pp. 327-341. ISSN: 0022-314X | doi: https://dx.doi.org/10.1016/j.jnt.2016.05.024
- Bondarenko, A. , Hilberdink, T. , Seip, K. (2016) Gál-type GCD sums beyond the critical line. Journal of Number Theory , 166 pp. 93-104. ISSN: 0022-314X | doi: https://dx.doi.org/10.1016/j.jnt.2016.02.017
- Al-Maamori, F. and Hilberdink, T. (2015) An example in Beurling's theory of generalised primes. Acta Arithmetica , 168 pp. 383-395. ISSN: 1730-6264 | doi: https://dx.doi.org/10.4064/aa168-4-4
- Hilberdink, T. (2015) An optimization problem concerning multiplicative functions. Linear Algebra and its Applications , 485 pp. 289-304. ISSN: 0024-3795 | doi: https://dx.doi.org/10.1016/j.laa.2015.07.005
- Hilberdink, T. (2015) Multiplicative Toeplitz matrices and the Riemann zeta function. In: Bringmann, K. , Bugeaud, Y. , Hilberdink, T. , Sander, J. , (eds.) Four faces of number theory. European Mathematical Society , Zurich. pp. 77-122. ISBN: 9783037191422 | doi: https://dx.doi.org/10.4171/142
- Hilberdink, T. (2014) The group of squarefree integers. Linear Algebra and its Applications , 457 pp. 383-399. ISSN: 0024-3795 | doi: https://dx.doi.org/10.1016/j.laa.2014.05.037
- Hilberdink, T. (2014) Maximal order of a class of multiplicative functions. Annales Universitatis Scientarium Budapestinensis , 14 pp. 217-237. ISSN: 0138-9491
- Hilberdink, T. (2013) 'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function. Functiones et Approximatio: Commentarii Mathematici , 49 (2). pp. 201-220. ISSN: 0208-6573 | doi: https://dx.doi.org/10.7169/facm/2013.49.2.1
- Hilberdink, T. (2012) Generalised prime systems with periodic integer counting function. Acta Arithmetica , 152 (3). pp. 217-241. ISSN: 1730-6264 | doi: https://dx.doi.org/10.4064/aa152-3-1
- Hilberdink, T. (2011) Flows of Mellin transforms with periodic integrator. Journal de Theorie des Nombres de Bordeaux , 23 pp. 455-469. ISSN: 1246-7405
- Hilberdink, T. (2010) Ω-results for Beurling's zeta function and lower bounds for the generalised Dirichlet divisor problem. Journal of Number Theory , 130 (3). pp. 707-715. ISSN: 0022-314X | doi: https://dx.doi.org/10.1016/j.jnt.2009.09.008
- Hilberdink, T. (2009) An arithmetical mapping and applications to Ω-results for the Riemann zeta function. Acta Arithmetica , 139 pp. 341-367. ISSN: 1730-6264 | doi: https://dx.doi.org/10.4064/aa139-4-3
- Hilberdink, T. (2009) Asymptotic expansions for Taylor coefficients of the composition of two functions. Asymptotic Analysis , 63 (3). pp. 125-142. ISSN: 1875-8576 | doi: https://dx.doi.org/10.3233/ASY-2008-0926
- Hilberdink, T. (2008) On the zeros of a class of arithmetical entire functions. Acta Arithmetica , 131 (1). pp. 69-85. ISSN: 0065-1036 | doi: https://dx.doi.org/10.4064/aa131-1-6
- Hilberdink, T. (2007) Orders of growth of real functions. Real Analysis Exchange , 32 (2). pp. 359-390.
- Hilberdink, T. (2007) A lower bound for the Lindelöf function associated to generalized integers. Journal of Number Theory , 122 (2). pp. 336-341. ISSN: 0022-314x | doi: https://dx.doi.org/10.1016/j.jnt.2006.05.007
- Hilberdink, T. and Lapidus, M. (2006) Beurling zeta functions, generalised primes, and fractal membranes. Acta Applicandae Mathematicae , 94 (1). pp. 21-48. ISSN: 0167-8019
- Hilberdink, T. (2006) Determinants of Multiplicative Toeplitz Matrices. Acta Arithmetica , 125 pp. 265-284.
- Hilberdink, T. (2005) Well-behaved Beurling primes and integers. Journal Of Number Theory , 112 (2). pp. 332-344.
- Hilberdink, T. (2004) Some connections between Bernoulli convolutions and analytic number theory. In: Lapidus, M. and van Frankenhuijsen, M. , (eds.) Fractal geometry and applications: a jubilee of Benoît Mandelbrot. Proceedings of Symposia in Pure Mathematics American Mathematical Society (72). , San Diego, CA. pp. 233-271. ISBN: 82186374
- Hilberdink, T. , Whitehead, C. , Salvi, N. (2003) On a Problem on Generalised Fibonacci Cubes. Ars Combinatoria , 68 pp. 39-47.