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The singular series of a cubic form in many variables and a new proof of Davenport's Shrinking Lemma

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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OriginalspracheEnglisch
Seiten (von - bis)681-691
Seitenumfang11
FachzeitschriftBulletin of the London Mathematical Society
Jahrgang57
Ausgabenummer3
PublikationsstatusVeröffentlicht - 10 März 2025

Abstract

We study the singular series associated to a cubic form with integer coefficients. If the number of variables is at least 10, we prove the absolute convergence (and hence positivity) under the assumption of Davenport's Geometric Condition, improving on a result of Heath-Brown. For the case of nine variables, we give a conditional treatment. We also provide a new short and elementary proof of Davenport's Shrinking Lemma that has been a crucial tool in previous literature on this and related problems.

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The singular series of a cubic form in many variables and a new proof of Davenport's Shrinking Lemma. / Bernert, Christian.
in: Bulletin of the London Mathematical Society, Jahrgang 57, Nr. 3, 10.03.2025, S. 681-691.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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