关于权的不可容许系数2和（2k+1\）新形式的一个注记

IF 0.5 Q3 MATHEMATICS

Annales Mathematiques du Quebec Pub Date : 2021-06-16 DOI:10.1007/s40316-021-00168-4

Malik Amir, Andreas Hatziiliou

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引用次数: 1

摘要

设\（f（z）=q+\sum_｛n\ge2｝a（n）q^n\）是具有整数系数和平凡残差mod2 Galois表示的权重k归一化新形式。在Amir和Hong（关于模椭圆曲线和某些K3曲面的L-函数，Ramanujan J，2021）中，当n满足某些同余时，我们通过排除或定位它们的傅立叶系数a（n）的所有奇素数\（|\ell|<；100\），对\（k=2\）的结果进行了推广。我们还研究了奇权（k\ge1\）新形式的情况，其中nebentypus由二次Dirichlet特征给出。

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A short note on inadmissible coefficients of weight 2 and \(2k+1\) newforms

Let \(f(z)=q+\sum _{n\ge 2}a(n)q^n\) be a weight k normalized newform with integer coefficients and trivial residual mod 2 Galois representation. We extend the results of Amir and Hong in Amir and Hong (On L-functions of modular elliptic curves and certain K3 surfaces, Ramanujan J, 2021) for \(k=2\) by ruling out or locating all odd prime values \(|\ell |<100\) of their Fourier coefficients a(n) when n satisfies some congruences. We also study the case of odd weights \(k\ge 1\) newforms where the nebentypus is given by a quadratic Dirichlet character.

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来源期刊

Annales Mathematiques du Quebec MATHEMATICS-

CiteScore

1.10

自引率

0.00%

发文量

期刊介绍： The goal of the Annales mathématiques du Québec (formerly: Annales des sciences mathématiques du Québec) is to be a high level journal publishing articles in all areas of pure mathematics, and sometimes in related fields such as applied mathematics, mathematical physics and computer science. Papers written in French or English may be submitted to one of the editors, and each published paper will appear with a short abstract in both languages. History: The journal was founded in 1977 as „Annales des sciences mathématiques du Québec”, in 2013 it became a Springer journal under the name of “Annales mathématiques du Québec”. From 1977 to 2018, the editors-in-chief have respectively been S. Dubuc, R. Cléroux, G. Labelle, I. Assem, C. Levesque, D. Jakobson, O. Cornea. Les Annales mathématiques du Québec (anciennement, les Annales des sciences mathématiques du Québec) se veulent un journal de haut calibre publiant des travaux dans toutes les sphères des mathématiques pures, et parfois dans des domaines connexes tels les mathématiques appliquées, la physique mathématique et l''informatique. On peut soumettre ses articles en français ou en anglais à l''éditeur de son choix, et les articles acceptés seront publiés avec un résumé court dans les deux langues. Histoire: La revue québécoise “Annales des sciences mathématiques du Québec” était fondée en 1977 et est devenue en 2013 une revue de Springer sous le nom Annales mathématiques du Québec. De 1977 à 2018, les éditeurs en chef ont respectivement été S. Dubuc, R. Cléroux, G. Labelle, I. Assem, C. Levesque, D. Jakobson, O. Cornea.