Browsing NTNU Open by Author "Bondarenko, Andrii"

Now showing items 1-13 of 13

    • An investigation of sums with reciprocals of binomial coefficients 

      Steinberg, Jasper (Bachelor thesis, 2022)
      Abstract will be available on 2025-06-01

    • Dynamics and additive combinatorics 

      Snarvold, Morten (Master thesis, 2020)

    • Exponential Weighted Sums related to the Divisor and Circle Problems 

      Mcnulty, Henry David Feaver (Master thesis, 2018)
      The classical results of the Dirichlet Divisor Problem and Gauss' Circle Problem are examined, with required information on the Riemann Zeta function presented. In particular, the results derived from the weighted sums of ...

    • Extreme values of the Riemann zeta function and its argument 

      Bondarenko, Andrii; Seip, Kristian (Journal article; Peer reviewed, 2018)
      We combine our version of the resonance method with certain convolution formulas for ζ(s) and logζ(s) . This leads to a new Ω result for |ζ(1/2+it)| : The maximum of |ζ(1/2+it)| on the interval 1≤t≤T is at ...

    • Fourier Interpolation with Zeros of Zeta and L-Functions 

      Bondarenko, Andrii; Radchenko, Danylo; Seip, Kristian (Peer reviewed; Journal article, 2022)
      We construct a large family of Fourier interpolation bases for functions analytic in a strip symmetric about the real line. Interesting examples involve the nontrivial zeros of the Riemann zeta function and other L-functions. ...

    • Gal-type GCD sums beyond the critical line 

      Bondarenko, Andrii; Hilberdink, Titus; Seip, Kristian (Journal article; Peer reviewed, 2016)

    • GCD sums and complete sets of square-free numbers 

      Seip, Kristian; Bondarenko, Andrii (Journal article; Peer reviewed, 2015)

    • Highly Composite Numbers 

      Øverlier, Lars Magnus (Master thesis, 2022)
      Hovedresultatet for denne oppgaven er å vise at det kun finnes endelig mange tall \(n\) slik at både \(n\) og \(d(n)\) er ``antiprimtall", hvor \(d(n)\) er divisorfunksjonen. Gjennom hele oppgaven blir Bertrands postulat ...

    • Large greatest common divisor sums and extreme values of the Riemann zeta function 

      Bondarenko, Andrii; Seip, Kristian (Journal article; Peer reviewed, 2017)

    • Linear space properties of H^p spaces of Dirichlet series 

      Bondarenko, Andrii; Brevig, Ole Fredrik; Saksman, Eero; Seip, Kristian (Journal article; Peer reviewed, 2019)
      We study H p spaces of Dirichlet series, called H p , for the range 0 < p < ∞. We begin by showing that two natural ways to define H p coincide. We then proceed to study some linear space properties of H p . More specifically, ...

    • Note on the resonance method for the Riemann zeta function 

      Bondarenko, Andrii; Seip, Kristian (Journal article; Peer reviewed, 2018)
      We improve Montgomery’s Ω-results for |ζ(σ + it)| in the strip 1/2 σ 1 and give in particular lower bounds for the maximum of |ζ(σ+it)| on √ T ≤ t ≤ T that are uniform in σ. We give similar lower bounds for the maximum of ...

    • Pseudomoments of the Riemann zeta function 

      Bondarenko, Andrii; Brevig, Ole Fredrik; Saksman, Eero; Seip, Kristian; Zhao, Jing (Journal article; Peer reviewed, 2018)
      The 2kth pseudomoments of the Riemann zeta function ζ ( s ) are, following Conrey and Gamburd, the 2 k th integral moments of the partial sums of ζ ( s ) on the critical line. For fixed k > 1 / 2 , these moments are known ...

    • Spherical coverings and X-raying convex bodies of constant width 

      Bondarenko, Andrii; Prymak, Andriy; Radchenko, Danylo (Peer reviewed; Journal article, 2021)
      Bezdek and Kiss showed that existence of origin-symmetric coverings of unit sphere in En by at most 2n congruent spherical caps with radius not exceeding arccosn−12n−−−√ implies the X-ray conjecture and the illumination ...