Finite dimensional distributions for short incomplete Gauss sums

Akarsu, EMEK

doi:10.1016/j.jmaa.2025.129685

Finite dimensional distributions for short incomplete Gauss sums

Akarsu E. D.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.551, sa.2, 2025 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 551 Sayı: 2
Basım Tarihi: 2025
Doi Numarası: 10.1016/j.jmaa.2025.129685
Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

This paper investigates an equivalent principle to the weak invariance principle, with a focus on short incomplete Gauss sums. We establish a limit law for the finite-dimensional distributions (FDD) of these sums as the size parameter grows. Additionally, the study extends these findings to the limiting distribution of theta functions, building upon prior research by the author. This connection highlights the broader implications of the results in the context of homogeneous dynamics and modular forms. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.