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Kurlberg, Pärorcid.org/0000-0003-4734-5092

Open this publication in new window or tab >>A note on multiplicative automatic sequences### Klurman, Oleksiy

### Kurlberg, Pär

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 357, no 10, p. 752-755Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER, 2019
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:kth:diva-265162 (URN)10.1016/j.crma.2019.10.002 (DOI)000496915600002 ()2-s2.0-85073997485 (Scopus ID)
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##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

We prove that any q-automatic completely multiplicative function f: N -> C essentially coincides with a Dirichlet character. This answers a question of J.-P. Allouche and L. Gold-makher and confirms a conjecture of J. Bell, N. Bruin and M. Coons for completely multiplicative functions. Further, assuming GRH, the methods allow us to replace completely multiplicative functions with multiplicative functions.

QC 20191219

Available from: 2019-12-19 Created: 2019-12-19 Last updated: 2019-12-19Bibliographically approvedOpen this publication in new window or tab >>On the free path length distribution for linear motion in an n-dimensional box### Holmin, Samuel

### Kurlberg, Pär

### Månsson, Daniel

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 51, no 46, article id 465201Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

IOP PUBLISHING LTD, 2018
##### Keywords

free, path, length, distribution
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:kth:diva-246299 (URN)10.1088/1751-8121/aae5ee (DOI)000460029900001 ()2-s2.0-85055489270 (Scopus ID)
#####

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##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

KTH, School of Electrical Engineering and Computer Science (EECS), Electromagnetic Engineering.

We consider the distribution of free path lengths, or the distance between consecutive bounces of random particles, in an n-dimensional rectangular box. If each particle travels a distance R, then, as R -> infinity the free path length coincides with the distribution of the length of the intersection of a random line with the box (for a natural ensemble of random lines) and we give an explicit formula (piecewise real analytic) for the probability density function in dimension two and three. In dimension two we also consider a closely related model where each particle is allowed to bounce N times, as N -> infinity, and give an explicit (again piecewise real analytic) formula for its probability density function. Further, in both models we can recover the side lengths of the box from the location of the discontinuities of the probability density functions.

QC 20190321

Available from: 2019-03-22 Created: 2019-03-22 Last updated: 2019-05-13Bibliographically approvedOpen this publication in new window or tab >>Variation of the Nazarov-Sodin constant for random plane waves and arithmetic random waves### Kurlberg, Pär

### Wigman, Igor

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 330, p. 516-552Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

ACADEMIC PRESS INC ELSEVIER SCIENCE, 2018
##### Keywords

Nodal components, Nazarov-Sodin constant, Spectral measure, Weak-* topology, Continuity, Arithmetic random waves
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:kth:diva-249657 (URN)10.1016/j.aim.2018.03.026 (DOI)000431472100015 ()2-s2.0-85056237337 (Scopus ID)
#####

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##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

King's College London.

This is a manuscript containing the full proofs of results announced in [10], together with some recent updates. We prove that the Nazarov-Sodin constant, which up to a natural scaling gives the leading order growth for the expected number of nodal components of a random Gaussian field, genuinely depends on the field. We then infer the same for "arithmetic random waves", i.e. random toral Laplace eigenfunctions. (C) 2018 Elsevier Inc. All rights reserved.

QC 20190415

Available from: 2019-04-15 Created: 2019-04-15 Last updated: 2019-04-15Bibliographically approvedOpen this publication in new window or tab >>Superscars in the Seba billiard### Kurlberg, Pär

### Ueberschär, Henrik

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2017 (English)In: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, To appear in J. Eur. Math. Soc. (JEMS)Article in journal (Refereed) Accepted
##### National Category

Other Mathematics
##### Identifiers

urn:nbn:se:kth:diva-197970 (URN)
#####

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##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

QCR 20170117

Available from: 2016-12-09 Created: 2016-12-09 Last updated: 2017-11-29Bibliographically approvedOpen this publication in new window or tab >>Evidence for the Dynamical Brauer-Manin Criterion### Amerik, Ekaterina

### Kurlberg, Pär

### Nguyen, Khoa D.

### Towsley, Adam

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); ### Viray, Bianca

### Voloch, Jose Felipe

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_4_j_idt188_j_idt202",{id:"formSmash:j_idt184:4:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2016 (English)In: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 25, no 1, p. 54-65Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Taylor & Francis, 2016
##### Keywords

arithmetic dynamics, Brauer-Manin obstruction
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:kth:diva-180209 (URN)10.1080/10586458.2015.1056889 (DOI)000365894600005 ()2-s2.0-84948427877 (Scopus ID)
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##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).

Let phi: X -> X be a morphism of a variety over a number field K. We consider local conditions and a "Brauer-Manin" condition, defined by Hsia and Silverman, for the orbit of a point P is an element of X(K) to be disjoint from a subvariety V subset of X, i.e., for V boolean AND O-phi (P) = empty set. We provide evidence that the dynamical Brauer-Manin condition is sufficient to explain the lack of points in the intersection V boolean AND O-phi (P); this evidence stems from a probabilistic argument as well as unconditional results in the case of etale maps.

QC 20160119

Available from: 2016-01-19 Created: 2016-01-08 Last updated: 2017-11-30Bibliographically approvedOpen this publication in new window or tab >>On probability measures arising from lattice points on circles### Kurlberg, Pär

### Wigman, I.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2016 (English)In: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, p. 1-42Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematics
##### Identifiers

urn:nbn:se:kth:diva-186995 (URN)10.1007/s00208-016-1411-4 (DOI)000398175700005 ()2-s2.0-84964290788 (Scopus ID)
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##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

A circle, centered at the origin and with radius chosen so that it has non-empty intersection with the integer lattice (Formula presented.), gives rise to a probability measure on the unit circle in a natural way. Such measures, and their weak limits, are said to be attainable from lattice points on circles. We investigate the set of attainable measures and show that it contains all extreme points, in the sense of convex geometry, of the set of all probability measures that are invariant under some natural symmetries. Further, the set of attainable measures is closed under convolution, yet there exist symmetric probability measures that are not attainable. To show this, we study the geometry of projections onto a finite number of Fourier coefficients and find that the set of attainable measures has many singularities with a “fractal” structure. This complicated structure in some sense arises from prime powers—singularities do not occur for circles of radius (Formula presented.) if n is square free.

QC 20160520

Available from: 2016-05-20 Created: 2016-05-16 Last updated: 2017-04-28Bibliographically approvedOpen this publication in new window or tab >>Superscars for arithmetic toral point scatterers### Kurlberg, Pär

### Rosenzweig, Lior

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2016 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 349, no 1, p. 329-360Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer, 2016
##### National Category

Other Mathematics
##### Identifiers

urn:nbn:se:kth:diva-198016 (URN)10.1007/s00220-016-2749-x (DOI)000392061000007 ()2-s2.0-84992046642 (Scopus ID)
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##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

We investigate eigenfunctions of the Laplacian perturbed by a delta potential on the standard tori in dimensions . Despite quantum ergodicity holding for the set of "new" eigenfunctions we show that superscars occur-there is phase space localization along families of closed orbits, in the sense that some semiclassical measures contain a finite number of Lagrangian components of the form , for uniformly bounded from below. In particular, for both and , eigenfunctions fail to equidistribute in phase space along an infinite subsequence of new eigenvalues. For , we also show that some semiclassical measures have both strongly localized momentum marginals and non-uniform quantum limits (i.e., the position marginals are non-uniform). For , superscarred eigenstates are quite rare, but for we show that the phenomenon is quite common-with denoting the counting function for the new eigenvalues below x, there are eigenvalues with the property that any semiclassical limit along these eigenvalues exhibits superscarring.

QC 20161213

Available from: 2016-12-09 Created: 2016-12-09 Last updated: 2017-11-29Bibliographically approvedOpen this publication in new window or tab >>Non-universality of the Nazarov-Sodin constant### Kurlberg, Pär

### Wigman, Igor

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 353, no 2, p. 101-104Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematics
##### Identifiers

urn:nbn:se:kth:diva-161112 (URN)10.1016/j.crma.2014.09.026 (DOI)000349200000003 ()2-s2.0-84921048169 (Scopus ID)
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##### Funder

Swedish Research Council, 621-2011-5498EU, FP7, Seventh Framework Programme, 335141
##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

We prove that the Nazarov-Sodin constant, which up to a natural scaling gives the leading order growth for the expected number of nodal components of a random Gaussian field, genuinely depends on the field. We then infer the same for "arithmetic random waves", i.e. random toral Laplace eigenfunctions.

QC 20150323

Available from: 2015-03-23 Created: 2015-03-09 Last updated: 2017-12-04Bibliographically approvedOpen this publication in new window or tab >>On the fixed points of the map x→xx modulo a prime### Kurlberg, Pär

### Luca, F.

### Shparlinski, I. E.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 22, no 1, p. 141-168Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Statistics, Residues, NN
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:kth:diva-166913 (URN)000353050500008 ()2-s2.0-84927591623 (Scopus ID)
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##### Funder

Swedish Research CouncilKnut and Alice Wallenberg Foundation
##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

In this paper, we show that for almost all primes p there is an integer solution xε [2,p-1] to the congruence xx ≡ x (mod p). The solutions can be interpretated as fixed points of the map x→xx (mod p), and we study numerically and discuss some unexpected properties of the dynamical system associated with this map.

QC 20150529

Available from: 2015-05-29 Created: 2015-05-21 Last updated: 2017-12-04Bibliographically approvedOpen this publication in new window or tab >>On the Average Exponent of Elliptic Curves Modulo p### Freiberg, Tristan

### Kurlberg, Pär

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 2014 (English)In: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, Vol. 2014, no 8, p. 2265-2293Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Artin Conjecture, Reductions, Cyclicity, Fields
##### National Category

Other Mathematics
##### Identifiers

urn:nbn:se:kth:diva-136366 (URN)10.1093/imrn/rns280 (DOI)000334361600008 ()2-s2.0-84896337544 (Scopus ID)
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##### Funder

Swedish Research Council
##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

Given an elliptic curve E defined over <inline-graphic xlink:href="RNS280IM1" xmlns:xlink="http://www.w3.org/1999/xlink"/> and a prime p of good reduction, let <inline-graphic xlink:href="RNS280IM2" xmlns:xlink="http://www.w3.org/1999/xlink"/> denote the group of <inline-graphic xlink:href="RNS280IM3" xmlns:xlink="http://www.w3.org/1999/xlink"/>-points of the reduction of E modulo p, and let e(p) denote the exponent of this group. Assuming a certain form of the generalized Riemann hypothesis (GRH), we study the average of e(p) as <inline-graphic xlink:href="RNS280IM4" xmlns:xlink="http://www.w3.org/1999/xlink"/> ranges over primes of good reduction, and find that the average exponent essentially equals p center dot c(E), where the constant c(E)> 0 depends on E. For E without complex multiplication (CM), c(E) can be written as a rational number (depending on E) times a universal constant, <inline-graphic xlink:href="RNS280IM5" xmlns:xlink="http://www.w3.org/1999/xlink"/>, the product being over all primes q. Without assuming GRH, we can determine the average exponent when E has CM, as well as give an upper bound on the average in the non-CM case.

QC 20140228

Available from: 2013-12-04 Created: 2013-12-04 Last updated: 2017-12-06Bibliographically approved