A Note on the Fourier coefficients of half-integral weight modular forms

Narasimha Kumar; Soma Purkait

A Note on the Fourier coefficients of half-integral weight modular forms

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arxiv 1304.6586 v3 pith:LOVIXGK7 submitted 2013-04-24 math.NT

Narasimha Kumar , Soma Purkait This is my paper · ORCID

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In this note, we show that the algebraicity of the Fourier coefficients of half-integral weight modular forms can be determined by checking the algebraicity of the first few of them. We also give a necessary and sufficient condition for a half-integral weight modular form to be in Kohnen's +-subspace by considering only finitely many terms.

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Squarefree numbers in short intervals: explicit and formalized
math.NT 2026-08 conditional novelty 6.0 of 10

For intervals of length H = X^{1/5 - 2/90935 + ε}, the number of squarefree integers differs from (6/π²)H by at most an explicit constant times H X^{-ε/10^{25}}.

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