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THE FOURIER COEFFICIENTS OF Θ‐SERIES IN ARITHMETIC PROGRESSIONS
Author(s) -
Hu Guangwei,
Jiang Yujiao,
Lü Guangshi
Publication year - 2020
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/mtk.12006
Subject(s) - mathematics , fourier series , series (stratigraphy) , convolution (computer science) , arithmetic , cusp (singularity) , fourier sine and cosine series , cusp form , simple (philosophy) , pure mathematics , fourier transform , algebra over a field , fourier analysis , mathematical analysis , geometry , fractional fourier transform , computer science , paleontology , philosophy , epistemology , machine learning , artificial neural network , biology
In this paper, we first study the Fourier coefficients of Θ‐series in arithmetic progressions and its applications. Secondly, we introduce a rather simple argument to improve some results on the shifted convolution sums of the Fourier coefficients of a cusp form for S L ( 2 , Z ) or S L ( 3 , Z ) and a Θ‐series.
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