uu.seUppsala University Publications

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Computations of Eisenstein series on Fuchsian groupsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2008 (English)In: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 77, no 263, p. 1779-1800Article in journal (Refereed) Published
##### Abstract [en]

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

2008. Vol. 77, no 263, p. 1779-1800
##### Keyword [en]

automorphic forms, spectral theory, computational number theory; Fourier coefficients, explicit machine computations, Phillips-Sarnak conjecture, K-Bessel function, Teichmuller space
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:uu:diva-96279DOI: 10.1090/S0025-5718-08-02092-9ISI: 000257559400029OAI: oai:DiVA.org:uu-96279DiVA, id: diva2:170799
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Available from: 2007-10-10 Created: 2007-10-10 Last updated: 2017-12-14Bibliographically approved
##### In thesis

We present numerical investigations of the value distribution and distribution of Fourier coefficients of the Eisenstein series E(z, s) on arithmetic and non-arithmetic Fuchsian groups. Our numerics indicate a Gaussian limit value distribution for a real- valued rotation of E(z; s) as Res = 1/2, Im s -> , infinity and also, on non-arithmetic groups, a complex Gaussian limit distribution for E(z, s) when Res > , 1/2 near 1/2 and Im s -> , infinity at least if we allow Re s. 1/2 at some rate. Furthermore, on non-arithmetic groups and for fixed s with Re s = 1/2 near 1/2, our numerics indicate a Gaussian limit distribution for the appropriately normalized Fourier coefficients.

1. Computations of Automorphic Functions on Fuchsian Groups$(function(){PrimeFaces.cw("OverlayPanel","overlay170802",{id:"formSmash:j_idt781:0:j_idt788",widgetVar:"overlay170802",target:"formSmash:j_idt781:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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