On the Fourier coefficients of certain Hilbert modular forms |
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Authors: | Agnihotri Rishabh Chakraborty Kalyan |
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Institution: | 1.Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhunsi, Prayagraj, 211019, India ;2.KSCSTE-Kerala School of Mathematics, Kunnamangalam PO, Kozhikode, Kerala, 673571, India ; |
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Abstract: | We prove that given any \(\epsilon >0\), a non-zero adelic Hilbert cusp form \({\mathbf {f}}\) of weight \(k=(k_1,k_2,\ldots ,k_n)\in ({\mathbb {Z}}_+)^n\) and square-free level \(\mathfrak {n}\) with Fourier coefficients \(C_{{\mathbf {f}}}(\mathfrak {m})\), there exists a square-free integral ideal \(\mathfrak {m}\) with \(N(\mathfrak {m})\ll k_0^{3n+\epsilon }N(\mathfrak {n})^{\frac{6n^2+1}{2}+\epsilon }\) such that \(C_{{\mathbf {f}}}(\mathfrak {m})\ne 0\). The implied constant depends on \(\epsilon , F\). |
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