A real effective version of the Freĭman-Scourfield Theorem

Küfner, Tanja

dc.contributor.advisor	Brüdern, Jörg Prof. Dr.
dc.contributor.author	Küfner, Tanja
dc.date.accessioned	2025-11-04T17:42:27Z
dc.date.available	2025-11-11T00:50:05Z
dc.date.issued	2025-11-04
dc.identifier.uri	http://resolver.sub.uni-goettingen.de/purl?ediss-11858/16322
dc.identifier.uri	http://dx.doi.org/10.53846/goediss-11614
dc.format.extent	47	de
dc.language.iso	eng	de
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/
dc.subject.ddc	510	de
dc.title	A real effective version of the Freĭman-Scourfield Theorem	de
dc.type	doctoralThesis	de
dc.contributor.referee	Brüdern, Jörg Prof. Dr.
dc.date.examination	2025-09-12	de
dc.description.abstracteng	We study the solvability of a Diophantine equation with mixed real exponents for sufficiently large natural numbers. The connection to a condition on the sum over the reciprocals of the exponents was first shown by Freĭman and Scourfield and recently made effective by Brüdern and Wooley. We prove an effective statement for the case of real exponents, which involves flooring in the equation. To this end, we apply the theory of the Hardy-Littlewood circle method adapted to Diophantine inequalities. In the fourth chapter, we show a mean value estimate utilising diminishing ranges and prove a novel Weyl-type estimate for exponential sums with a non-integer exponent. The calculations on the arcs in the fifth chapter lead to conditions that are translated into the effective result in the last chapter.	de
dc.contributor.coReferee	Schindler, Damaris Prof. Dr.
dc.subject.eng	Analytic number theory	de
dc.subject.eng	Diophantine equations	de
dc.subject.eng	Diophantine inequalities	de
dc.subject.eng	Hardy-Littlewood circle method	de
dc.subject.eng	Freĭman-Scourfield theorem	de
dc.subject.eng	Non-integer exponents	de
dc.identifier.urn	urn:nbn:de:gbv:7-ediss-16322-6
dc.affiliation.institute	Fakultät für Mathematik und Informatik	de
dc.subject.gokfull	Mathematics (PPN61756535X)	de
dc.description.embargoed	2025-11-11	de
dc.identifier.ppn	1940264510
dc.notes.confirmationsent	Confirmation sent 2025-11-04T19:45:01	de

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