M. Asgari and R. Schmidt, Siegel modular forms and representations, manuscripta mathematica, vol.104, issue.2, pp.173-200, 2001.
DOI : 10.1007/PL00005869

B. C. Berndt, Identities involving the coefficients of a class of Dirichlet series. V, Transactions of the American Mathematical Society, vol.160, pp.139-156, 1971.
DOI : 10.1090/S0002-9947-71-99991-0

K. Chandrasekharan and &. R. Narasimhan, Functional Equations With Multiple Gamma Factors and the Average Order of Arithmetical Functions, The Annals of Mathematics, vol.76, issue.1, pp.93-136, 1962.
DOI : 10.2307/1970267

K. Chandrasekharan and &. R. Narasimhan, The approximate functional equation for a class of zeta-functions, Mathematische Annalen, vol.9, issue.2, pp.30-64, 1963.
DOI : 10.1007/BF01343729

J. B. Conrey and &. A. Ghosh, On the Selberg class of Dirichlet series: small degrees, Duke Math, J, vol.72, pp.673-693, 1993.

J. L. Hafner, On the representation of the summatory functions of a class of arithmetical functions, Lecture Notes in Math, vol.48, issue.3, pp.148-165, 1980.
DOI : 10.2307/1969179

D. R. Heath-brown and &. Tsang, Sign Changes of E(T), ??(x), and P(x), Journal of Number Theory, vol.49, issue.1, pp.73-83, 1994.
DOI : 10.1006/jnth.1994.1081

H. H. Kim, Functoriality for the exterior square of GL 4 and symmetric fourth of GL 2 , With appendix 1 by D. Ramakrishnan and appendix 2 by, Math. Soc, pp.16-139, 2003.

H. H. Kim and &. P. Sarnak, Refined estimates towards the Ramanujan and Selberg conjectures, J. Amer. Math. Soc, vol.16, issue.1, pp.175-183, 2003.

Y. Lau, On the Mean Square Formula of the Error Termfor a Class of Arithmetical Functions, Monatshefte f???r Mathematik, vol.128, issue.2, pp.111-129, 1999.
DOI : 10.1007/s006050050050

Y. Lau, J. Liu, and &. J. Wu, Sign changes of the coefficients of automorphic L-functions, Number Theory: Arithmetic In, pp.141-181, 2013.

Y. Lau and &. Tsang, Large values of error terms of a class of arithmetical functions, Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.2002, issue.544, pp.25-38, 2002.
DOI : 10.1515/crll.2002.026

J. Liu, Y. Qu, and &. J. Wu, Two Linnik-type problems for automorphic L-functions, Mathematical Proceedings of the Cambridge Philosophical Society, vol.151, issue.02, pp.219-227, 2011.
DOI : 10.1016/j.jnt.2009.08.015

URL : https://hal.archives-ouvertes.fr/hal-01277862

J. Liu and &. J. Wu, The number of coefficients of automorphic L-functions for <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:msub><mml:mrow><mml:mi mathvariant="italic">GL</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msub></mml:math> of same signs, Journal of Number Theory, vol.148, pp.429-450, 2015.
DOI : 10.1016/j.jnt.2014.09.020

W. Luo, Z. Rudnick, and &. P. Sarnak, On the generalized Ramanujan conjecture for GL m, Proceedings of Symposia In Pure Mathematics, pp.301-310, 1999.

K. Matomäki and &. , Radziwii ll l, Sign changes of Hecke eigenvalues

J. Meher and &. M. Murty, Sign changes of Fourier coefficients of half-integral weight cusp forms, International Journal of Number Theory, vol.10, issue.04, pp.905-914, 2014.
DOI : 10.1142/S1793042114500067

S. Mizumoto, Poles and residues of standardL-functions attached to Siegel modular forms, Mathematische Annalen, vol.8, issue.1, pp.589-612, 1991.
DOI : 10.1007/BF01446591

G. Molteni, A note on a result of Bochner and Conrey-Ghosh about the Selberg class, Archiv der Mathematik, vol.72, issue.3, pp.219-222, 1999.
DOI : 10.1007/s000130050325

E. Royer, J. Sengupta, and J. Wu, SIGN CHANGES IN SHORT INTERVALS OF COEFFICIENTS OF SPINOR ZETA FUNCTION OF A SIEGEL CUSP FORM OF GENUS 2, International Journal of Number Theory, vol.10, issue.02, pp.327-339, 2014.
DOI : 10.1142/S1793042113500966

URL : https://hal.archives-ouvertes.fr/hal-01093998

Z. Rudnick and &. P. Sarnak, Zeros of principal L-functions and random matrix theory, Duke Math, J, vol.81, pp.269-322, 1996.

R. Schmidt, On the Archimedean Euler Factors for Spin L- Functions, Abhandlungen aus dem Mathematischen Seminar der Universit??t Hamburg, vol.33, issue.3, pp.119-162, 2002.
DOI : 10.1007/BF02941668

G. Shimura, On Modular Forms of Half Integral Weight, The Annals of Mathematics, vol.97, issue.3, pp.440-481, 1973.
DOI : 10.2307/1970831

Y. Lau, Pokfulam Road, Hong Kong E-mail address: yklau@maths.hku

J. Wu, C. , and I. Cartan-de-lorraine, F-54506 Vandoeuvrel` es, p.54506