Browsing NTNU Open by Author "Seip, Kristian"

Now showing items 1-20 of 49

    • A Brief Introduction to the Theory of Prolate Spheroidal Wave Functions 

      Rønseth, Maximilian. (Bachelor thesis, 2023)
      Vi går gjennom deler av Slepians artikkel ``Some comments on Fourier analysis, uncertainty and modelling" og prøver og forstå noen grunnleggende detaljer om prolate sfærisk bølgefunsksjoner. Vi legger til ekstra detaljer ...

    • A Conditional Bound for the Riemann zeta-function in the Critical Line 

      Tell, William (Master thesis, 2022)
      Denne oppgaven bestemmer eksplisitte konstanter for den øvre begrensningen av logaritmen til Riemann zeta-funksjonen på den kritiske linja, under antakelsen av Riemann-hypotesen. Dette krever to betraktninger. Vi finner ...

    • Aleksei Fourier Interpolation and Contractive Inequalities 

      Kulikov, Aleksei (Doctoral theses at NTNU;2022:209, Doctoral thesis, 2022)

    • An introduction to primes in short intervals 

      Fissum, Robin (Master thesis, 2023)
      I denne oppgaven gir vi en introduksjon til studiet av primtall i korte intervaller: Primtallsatsen er ekvivalent med utsagnet om at antall primtall i intervallet (x, x + h] er asymptotisk med h / log x når h = x, og vi ...

    • Approximation numbers of composition operators on H^p spaces of Dirichlet series 

      Bayart, Frederic; Queffelec, Herve; Seip, Kristian (Journal article; Peer reviewed, 2016)
      By a theorem of the first named author, $\varphi $ generates a bounded composition operator on the Hardy space ${\mathscr{H}}^p$of Dirichlet series $(1\le p<\infty )$ only if $\varphi (s)=c_0 s+\psi (s)$, where $c_0$ is a ...

    • Aspects of Dirichlet series: Composition operators, Bohr’s theorem and universality 

      Kouroupis, Athanasios (Doctoral theses at NTNU;2024:181, Doctoral thesis, 2024)

    • Contractive inequalities for Hardy spaces 

      Brevig, Ole Fredrik; Ortega-Cerdà, Joaquim; Seip, Kristian; Zhao, Jing (Journal article; Peer reviewed, 2018)
      We state and discuss several interrelated results, conjectures, and questions regarding contractive inequalities for classical Hp spaces of the unit disc. We study both coefficient estimates in terms of weighted ℓ 2 sums ...

    • Convergence of series of dilated functions and spectral norms of GCD matrices 

      Seip, Kristian; Aistleitner, Christoph; Berkes, Istvan; Weber, Michel (Journal article; Peer reviewed, 2015)

    • A converse to the Schwarz lemma for planar harmonic maps 

      Brevig, Ole Fredrik; Ortega-Cerdà, Joaquim; Seip, Kristian (Peer reviewed; Journal article, 2021)
      A sharp version of a recent inequality of Kovalev and Yang on the ratio of the (H1)∗ and H4 norms for certain polynomials is obtained. The inequality is applied to establish a sharp and tractable sufficient condition for ...

    • Decay rates for approximation numbers of composition operators 

      Queffelec, Herve; Seip, Kristian (Journal article; Peer reviewed, 2015)
      A general method for estimating the approximation numbers of composition operators on the Hardy space H 2, using finite-dimensional model subspaces, is studied and applied in the case when the symbol of the operator maps ...

    • Den Cramér-stokastiske modellen for primtala 

      Svela, Erling Arnold Tønseth (Bachelor thesis, 2020)
      Målet med denne oppgåva er å introdusera Cramér-modellen, og å drøfta om den modellerer primtala på ein rimeleg måte. Motivasjonen bak modellen vert forklart og modellen vert definert. Somme av krava modellar av primtala ...

    • A dichotomy for extreme values of zeta and Dirichlet L-functions 

      Bondarenko, Andrii; Darbar, Pranendu; Hagen, Markus Valås; Heap, Paul Winston; Seip, Kristian (Peer reviewed; Journal article, 2023)
      We exhibit large values of the Dedekind zeta function of a cyclotomic field on the critical line. This implies a dichotomy whereby one either has improved lower bounds for the maximum of the Riemann zeta function, or large ...

    • Digit sums and the number of prime factors of the factorial n!=1·2···n 

      Fissum, Robin (Bachelor thesis, 2020)
      Vi utleder en asymptotisk formel for tverrsummer, og viser hvordan den kan brukes til å estimere det totale antallet primfaktorer av n!=1·2···n (n fakultet). Vi gir også en kort oppsummering av historien bak problemet, og ...

    • Does Nehari's Theorem Hold in Dimension Two? - Some Numerical Experiments. 

      Bortheim, Camilla Fluge (Master thesis, 2023)
      I denne oppgåva prøver vi å finne eit moteksempel til Nehari sitt teorem i to dimensjonar. Dette vert gjort ved å bruke numeriske utrekningar for å auke den nedre grensa til $C_2$. Her er $C_2$ det minste reelle talet slik ...

    • Et dypdykk i Riemann zetafunksjonens maksimum på 1-linjen: Innsikter fra Winston Heaps artikkel 

      Taraldsen, Emil Dalen (Master thesis, 2023)
      I denne oppgaven skal jeg se på Winston Heaps artikkel "A note on the maximum of the Riemann zeta function on the 1-line". Jeg skal forsøksvis gi en dypere og mer detaljert forklaring på hva som kobler maksimumet av Riemann ...

    • Extreme values of the argument of the Riemann zeta function 

      Hagen, Markus Valås (Master thesis, 2023)
      Vi beviser et eksplisitt Ω-resultat for argumentet til Riemann’s zeta funksjon. Deretter finner vi store verdier av argumentet til Dedekind zeta funksjonen til en syklotomisk kropp. Dette resulterer i forbedrete Ω-resultat ...

    • 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 ...

    • A footnote to a theorem Halász 

      Saias, Eric; Seip, Kristian (Journal article; Peer reviewed, 2020)
      We study multiplicative functions f satisfying |f(n)|≤1 for all n, the associated Dirichlet series F(s):=∑∞n=1f(n)n−s, and the summatory function Sf(x):=∑n≤xf(n). Up to a possible trivial contribution from the numbers ...

    • 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)