| 1. |
- Fiorilli, Daniel, et al.
(author)
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Low-lying zeros of quadratic Dirichlet L-functions : lower order terms for extended support
- 2017
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In: Compositio Mathematica. - : Cambridge University Press. - 0010-437X .- 1570-5846. ; 153:6, s. 1196-1216
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Journal article (peer-reviewed)abstract
- We study the 1-level density of low-lying zeros of Dirichlet L-functions attached to real primitive characters of conductor at most X. Under the generalized Riemann hypothesis, we give an asymptotic expansion of this quantity in descending powers of log X, which is valid when the support of the Fourier transform of the corresponding even test function phi is contained in (-2, 2). We uncover a phase transition when the supremum sigma of the support of (phi) over cap reaches 1, both in the main term and in the lower order terms. A new lower order term appearing at sigma = 1 involves the quantity (phi) over cap (1), and is analogous to a lower order term which was isolated by Rudnick in the function field case.
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| 2. |
- Fiorilli, Daniel, et al.
(author)
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Low-lying zeros of quadratic Dirichlet L-functions: A transition in the ratios conjecture
- 2018
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In: Quarterly Journal of Mathematics. - : Oxford University Press (OUP). - 0033-5606 .- 1464-3847. ; 69:4, s. 1129-1149
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Journal article (peer-reviewed)abstract
- We study the 1-level density of low-lying zeros of quadratic Dirichlet L-functions by applying the L-functions Ratios Conjecture. We observe a transition in the main term as was predicted by the Katz-Sarnak heuristic as well as in the lower-order terms when the support of the Fourier transform of the corresponding test function reaches the point 1. Our results are consistent with those obtained in previous work under GRH and are furthermore analogous to results of Rudnick in the function field case.
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| 3. |
- Fiorilli, D., et al.
(author)
-
Low-lying zeros of quadratic Dirichlet L-functions: lower order terms for extended support
- 2017
-
In: Compositio Mathematica. - : Wiley. - 0010-437X .- 1570-5846. ; 153:6, s. 1196-1216
-
Journal article (peer-reviewed)abstract
- We study the 1-level density of low-lying zeros of Dirichlet L-functions attached to real primitive characters of conductor at most X. Under the generalized Riemann hypothesis, we give an asymptotic expansion of this quantity in descending powers of log X, which is valid when the support of the Fourier transform of the corresponding even test function phi is contained in (-2, 2). We uncover a phase transition when the supremum sigma of the support of (phi) over cap reaches 1, both in the main term and in the lower order terms. A new lower order term appearing at sigma = 1 involves the quantity (phi) over cap (1), and is analogous to a lower order term which was isolated by Rudnick in the function field case.
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| 4. |
- Shankar, A., et al.
(author)
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SATO-TATE EQUIDISTRIBUTION OF CERTAIN FAMILIES OF ARTIN L-FUNCTIONS
- 2019
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In: Forum of Mathematics Sigma. - : Cambridge University Press (CUP). - 2050-5094. ; 7
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Journal article (peer-reviewed)abstract
- We study various families of Artin L-functions attached to geometric parametrizations of number fields. In each case we find the Sato-Tate measure of the family and determine the symmetry type of the distribution of the low-lying zeros.
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| 5. |
- Strömbergsson, Andreas, 1973-, et al.
(author)
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On the generalized circle problem for a random lattice in large dimension
- 2019
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In: Advances in Mathematics. - : Elsevier BV. - 1090-2082 .- 0001-8708. ; 345, s. 1042-1074
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Journal article (peer-reviewed)abstract
- In this note we study the error term R-n,R-L(x) in the generalized circle problem for a ball of volume x and a random lattice L of large dimension n. Our main result is the following functional central limit theorem: Fix an arbitrary function f : Z(+) -> R+ satisfying lim(n ->infinity) f (n) = infinity and f (n) = O-epsilon(e(epsilon n)) for every epsilon > 0. Then, the random function t bar right arrow 1/root 2f (n) R-n,R-L (t f(n)) on the interval [0, 1] converges in distribution to one-dimensional Brownian motion as n -> infinity. The proof goes via convergence of moments, and for the computations we develop a new version of Rogers' mean value formula from [18]. For the individual kth moment of the variable (2f (n))(-1/2) R-n,R-L (f (n)) we prove convergence to the corresponding Gaussian moment more generally for functions f satisfying f (n) = O(e(cn)) for any fixed c is an element of (0, c(k)), where c(k) is a constant depending on k whose optimal value we determine. (C) 2019 Elsevier Inc. All rights reserved.
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| 6. |
- Strömbergsson, Andreas, 1973-, et al.
(author)
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On the location of the zero-free half-plane of a random Epstein zeta function
- 2018
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In: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 371:3-4, s. 1191-1227
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Journal article (peer-reviewed)abstract
- In this note we study, for a random lattice L of large dimension n, the supremum of the real parts of the zeros of the Epstein zeta function and prove that this random variable scaled by has a limit distribution, which we give explicitly. This limit distribution is studied in some detail; in particular we give an explicit formula for its distribution function. Furthermore, we obtain a limit distribution for the frequency of zeros of in vertical strips contained in the half-plane n/2.
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| 7. |
- Wahlin, Bengt, 1977-
(author)
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Atherosclerotic cardiovascular disease in rheumatoid arthritis : aspects of pathogenesis and risk
- 2019
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Doctoral thesis (other academic/artistic)abstract
- Patients with rheumatoid arthritis (RA) have an increased prevalence and severity of atherosclerosis, and a corresponding increased risk of cardiovascular disease. The mechanisms causing this are not well elucidated, but both traditional cardiovascular risk factors and RA-associated factors have been associated with atherosclerosis and increased risk of cardiovascular events in patients with RA. Cardiovascular risk estimation based on traditional cardiovascular risk factors, often underestimates the risk in patients with RA. The aims of this thesis were to examine factors and biomarkers associated with atherosclerosis in patients with RA, and to evaluate an algorithm for cardiovascular risk estimation in patients with RA.Methods Patients with early RA in the four northernmost counties of Sweden have since 1995 been included in a prospective study of both the progress of RA and comorbidities. Besides clinical data, radiographs, genetic markers and autoantibodies are registered. Paper I includes 665 patients aged 40-80 years from that cohort, in whom the 10-year risk of a first cardiovascular event was estimated with both Expanded Cardiovascular Risk Prediction Score in Rheumatoid Arthritis (ERS-RA), and the general population based ACC/AHA algorithm. The estimations were then compared to the actual outcomes. Paper II examines factors associated with coronary artery calcification (CAC) in 22 patients with long-standing RA. Papers III and IV use data from a cohort of patients <60 years of age at diagnosis of RA (n=79), in whom development of atherosclerosis has been prospectively followed since diagnosis of RA. This is a subset of patients from the larger cohort in paper I. Controls matched for age and sex (n=44) are examined as well. In paper III, phenotypes of T-cells and IgG-antibodies against cytomegalovirus (CMV) are analysed in relation to carotid intima-media thickness (IMT). In paper IV, bone mineral density and markers and regulators of bone metabolism are analysed in relation to IMT.Results Cardiovascular risk estimation with the RA-specific algorithm ERS-RA is not superior to estimation with the ACC/AHA algorithm. Both algorithms underestimate the risk in patients with a high grade of inflammation and in patients with an estimated moderate risk. In patients with long-standing RA, presence of CAC is associated with inflammatory activity, both at time of examination and in earlier stages of RA. Presence of anti-CMV IgG antibodies and altered T-cells (both CD4+ and CD8+) lacking the co-stimulatory molecule CD28 (CD28null) are associated with a higher IMT, and patients IgG-positive for CMV have a rapid increase in IMT after onset of RA. Regulators of bone metabolism (sclerostin, osteoprotegerin and osteocalcin) are associated with a higher IMT in patients with RA.Conclusion Cardiovascular risk estimation in patients with RA still needs to be improved. The fact that CMV-positivity, altered populations of T-cells and IMT all are associated, and that also regulators of bone metabolism reflect IMT, suggests that the pathogenesis of atherosclerosis in patients with RA is multifactorial. This thesis provides knowledge of the accelerated development of atherosclerosis in RA and could possibly be relevant also in other chronic inflammatory diseases, where markers of accelerated atherosclerosis and increased cardiovascular risk are lacking.
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