Sign changes in restricted coefficients of Hilbert modular forms

被引：0

作者：

Agnihotri, Rishabh ^{[1
,2
]}

Chakraborty, Kalyan ^{[3
]}

Krishnamoorthy, Krishnarjun ^{[2
]}

机构：

[1] Indian Inst Sci, Bangalore 560012, Karnataka, India

[2] A CI Homi Bhabha Natl Inst, Harish Chandra Res Inst, Chhatnag Rd, Prayagraj 211019, India

[3] KCSTE, Kerala Sch Math, Kozhikode 673571, Kerala, India

来源：

RAMANUJAN JOURNAL | 2022年 / 59卷 / 04期

关键词：

Sign changes; Hilbert modular forms; Arithmetic progressions; Square-free coefficients; FOURIER-COEFFICIENTS;

D O I：

10.1007/s11139-022-00594-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let f be an adelic Hilbert cusp form of weight k and level n over a totally real number field F. In this paper, we study the sign changes in the Fourier coefficients of f when restricted to square-free integral ideals and integral ideals in "arithmetic progression". In both cases we obtain qualitative results and in the former case we obtain a quantitative result as well. Our results are general in the sense that we do not impose any restriction to the totally real number field F, the weight k or the level n.

引用

页码：1225 / 1243

页数：19

共 20 条

[1] On the Fourier coefficients of certain Hilbert modular forms [J].

Agnihotri, Rishabh ;

Chakraborty, Kalyan .

RAMANUJAN JOURNAL, 2022, 58 (01) :167-182

[2]

Apostol TM., 1976, INTRO ANAL NUMBER TH, DOI DOI 10.1007/978-1-4757-5579-4

[3] A note on signs of Fourier coefficients of two cusp forms [J].

Banerjee, S. .

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2018, 128 (04)

[4]

Blasius D., 2006, Noncommutative Geometry and Number Theory, P35

[5]

Garrett P., 1990, Holomorphic Hilbert Modular Forms

[6] Simultaneous sign change of Fourier-coefficients of two cusp forms [J].

Gun, Sanoli ;

Kohnen, Winfried ;

Rath, Purusottam .

ARCHIV DER MATHEMATIK, 2015, 105 (05) :413-424

[7]

Harcos G, 2002, INT MATH RES NOTICES, V2002, P923

[8] THE SIGN OF FOURIER COEFFICIENTS OF HALF-INTEGRAL WEIGHT CUSP FORMS [J].

Hulse, Thomas A. ;

Kiral, E. Mehmet ;

Kuan, Chan Ieong ;

Lim, Li-Mei .

INTERNATIONAL JOURNAL OF NUMBER THEORY, 2012, 8 (03) :749-762

[9] Simultaneous behaviour of the Fourier coefficients of two Hilbert modular cusp forms [J].

Kaushik, Surjeet ;

Kumar, Narasimha .

ARCHIV DER MATHEMATIK, 2019, 112 (03) :241-248

[10] Sign changes of Fourier coefficients of cusp forms supported on prime power indices [J].

Kohnen, Winfried ;

Martin, Yves .

INTERNATIONAL JOURNAL OF NUMBER THEORY, 2014, 10 (08) :1921-1927

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