Geodesic
SIGN CHANGES OF FOURIER COEFFICIENTS OF ENTIRE MODULAR INTEGRALS
Glasgow mathematical journal, Tome 54 (2012) no. 2, pp. 355-358

Voir la notice de l'article provenant de la source Cambridge University Press

Let f be a non-zero cusp form with real Fourier coefficients a(n) (n ≥ 1) of positive real weight k and a unitary multiplier system v on a subgroup Γ ⊂ SL2(R) that is finitely generated and of Fuchsian type of the first kind. Then, it is known that the sequence (a(n))(n ≥ 1) has infinitely many sign changes. In this short note, we generalise the above result to the case of entire modular integrals of non-positive integral weight k on the group Γ0*(N) (N ∈ N) generated by the Hecke congruence subgroup Γ0(N) and the Fricke involution provided that the associated period functions are polynomials.
DOI : 10.1017/S0017089512000018
Mots-clés : Primary 11F03, 11F99 
CHOIE, YOUNGJU; KOHNEN, WINFRIED. SIGN CHANGES OF FOURIER COEFFICIENTS OF ENTIRE MODULAR INTEGRALS. Glasgow mathematical journal, Tome 54 (2012) no. 2, pp. 355-358. doi: 10.1017/S0017089512000018
@article{10_1017_S0017089512000018,
     author = {CHOIE, YOUNGJU and KOHNEN, WINFRIED},
     title = {SIGN {CHANGES} {OF} {FOURIER} {COEFFICIENTS} {OF} {ENTIRE} {MODULAR} {INTEGRALS}},
     journal = {Glasgow mathematical journal},
     pages = {355--358},
     year = {2012},
     volume = {54},
     number = {2},
     doi = {10.1017/S0017089512000018},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000018/}
}
TY  - JOUR
AU  - CHOIE, YOUNGJU
AU  - KOHNEN, WINFRIED
TI  - SIGN CHANGES OF FOURIER COEFFICIENTS OF ENTIRE MODULAR INTEGRALS
JO  - Glasgow mathematical journal
PY  - 2012
SP  - 355
EP  - 358
VL  - 54
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000018/
DO  - 10.1017/S0017089512000018
ID  - 10_1017_S0017089512000018
ER  - 
%0 Journal Article
%A CHOIE, YOUNGJU
%A KOHNEN, WINFRIED
%T SIGN CHANGES OF FOURIER COEFFICIENTS OF ENTIRE MODULAR INTEGRALS
%J Glasgow mathematical journal
%D 2012
%P 355-358
%V 54
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000018/
%R 10.1017/S0017089512000018
%F 10_1017_S0017089512000018

[1] 1.Bol, G., Invarianten linearer differential gleichungen, Abh. Math. Sem. Univ. Hamburg. 16 (3–4) (1949), 1–28. Google Scholar

[2] 2.Knopp, M., Modular integrals on Γ(N) and Dirichlet series with functional equations, in Number theory (Chudnovsky, D. V. et al. Editors) (Springer, Berlin, Germany, 1985), 211–224. Lect. No. 1135. Google Scholar | DOI

[3] 3.Knopp, M., Kohnen, W. and Pribitkin, W., On the signs of Fourier coefficients of cusp forms, Ramanujan J. 7 (2003), 269–277. Google Scholar | DOI

[4] 4.Kohnen, W., On the growth of the Petersson norms of Fourier-Jacobi coefficients of Siegel cusp forms, Bull. Lond. Math. Soc. 43 (4) (2011), 717–720. Google Scholar | DOI

[5] 5.Landau, E., Uber einen Satz von Tschebyschef, Math. Ann. 61 (1906), 527–550. Google Scholar | DOI

Cité par Sources :