A. N. Andrianov and V. G. Zhuravlëv, Modular forms and Hecke operators, Translations of Mathematical Monographs, p.11045, 1995.

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

T. Berger, Siegel paramodular forms of degree two attached to Bianchi modular forms

S. Breulmann, On Hecke eigenforms in the Maa?? space, Mathematische Zeitschrift, vol.232, issue.3, pp.527-530, 1999.
DOI : 10.1007/PL00004769

S. Das, ON THE NATURAL DENSITIES OF EIGENVALUES OF A SIEGEL CUSP FORM OF DEGREE 2, International Journal of Number Theory, vol.09, issue.01, pp.9-15, 2013.
DOI : 10.1142/S1793042112501217

S. Das, W. Kohnen, and J. Sengupta, On a convolution series attached to a Siegel Hecke cusp form of degree 2, The Ramanujan Journal, vol.54, issue.2, pp.367-378, 2014.
DOI : 10.1007/s11139-013-9495-x

V. Luis and . Dieulefait, On the images of the Galois representations attached to genus 2 Siegel modular forms, J. Reine Angew. Math, vol.553, pp.183-200, 2002.

D. T. Peter, J. Elliott, and . Kish, Harmonic Analysis on the Positive Rationals II: Multiplicative Functions and Maass Forms, 2014.

P. Erd?s, On the difference of consecutive terms of sequences defined by divisibility properties, Acta Arith, vol.12, pp.175-182, 1966.

R. R. Hall and G. Tenenbaum, Effective mean value estimates for complex multiplicative functions, Mathematical Proceedings of the Cambridge Philosophical Society, vol.48, issue.02, pp.337-351, 1991.
DOI : 10.1112/jlms/s2-30.3.394

J. Johnson-leung and B. Roberts, Siegel modular forms of degree two attached to Hilbert modular forms, Journal of Number Theory, vol.132, issue.4, pp.543-564, 2012.
DOI : 10.1016/j.jnt.2011.08.004

C. Khare and J. Wintenberger, Serre's modularity conjecture. I, Invent, Math, vol.178, issue.3, pp.485-504, 2009.
DOI : 10.1142/9789814324359_0051

W. Kohnen, Sign changes of Hecke eigenvalues of Siegel cusp forms of genus two, Proceedings of the American Mathematical Society, vol.135, issue.04, pp.997-999, 2007.
DOI : 10.1090/S0002-9939-06-08570-4

E. Kowalski, O. Robert, and J. Wu, Small gaps in coefficients of $L$-functions and $\mathfrak{B}$-free numbers in short intervals, Revista Matem??tica Iberoamericana, vol.23, issue.1, pp.281-326, 2007.
DOI : 10.4171/RMI/496

J. Liu and J. Wu, The number of coefficients of automorphic L-functions for GL m of same signs, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01278944

K. Matomäki and M. Radziwill, Sign changes of Hecke eigenvalues, Geometric and Functional Analysis, vol.64, issue.2, 2014.
DOI : 10.1007/s00039-015-0350-7

H. Narita, A. Pitale, and R. Schmidt, Irreducibility criteria for local and global representations, Proc. Amer, pp.55-63, 2013.
DOI : 10.1090/S0002-9939-2012-11438-8

A. Pitale, A. Saha, and R. Schmidt, Transfer of Siegel cusp forms of degree 2, Mem. Amer, Math. Soc, vol.232, issue.1090, p.107, 2014.

A. Pitale and R. Schmidt, Sign changes of Hecke eigenvalues of Siegel cusp forms of degree $2$, Proceedings of the American Mathematical Society, vol.136, issue.11, pp.3831-3838, 2008.
DOI : 10.1090/S0002-9939-08-09364-7

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

J. Serre, Quelques applications du théorème de densité de Chebotarev, Inst. Hautes Études Sci. Publ. Math, vol.83, issue.54, pp.323-401, 1981.
DOI : 10.1007/bf02698692

S. Joung-min, Sums of nonnegative multiplicative functions over integers without large prime factors. I, Acta Arith, pp.329-351, 2001.

G. Tenenbaum, Introduction to analytic and probabilistic number theory, Cambridge Studies in Advanced Mathematics, vol.163, p.11005, 1995.
DOI : 10.1090/gsm/163
URL : https://hal.archives-ouvertes.fr/hal-01281339

R. Weissauer, Endoscopy for GSp(4) and the cohomology of Siegel modular threefolds, Four dimensional Galois representations Formes automorphes. II. Le cas du groupe GSp, pp.67-150, 2005.
DOI : 10.1007/978-3-540-89306-6

J. Wu and Y. Ye, Hypothesis H and the prime number theorem for automorphic representations, Functiones et Approximatio Commentarii Mathematici, vol.37, issue.2, pp.461-471, 2007.
DOI : 10.7169/facm/1229619665
URL : https://hal.archives-ouvertes.fr/hal-00097153

J. Wu and W. Zhai, DISTRIBUTION OF HECKE EIGENVALUES OF NEWFORMS IN SHORT INTERVALS, The Quarterly Journal of Mathematics, vol.64, issue.2, pp.619-644, 2013.
DOI : 10.1093/qmath/has007
URL : https://hal.archives-ouvertes.fr/hal-01278937

D. Zagier, Sur la conjecture de Saito-Kurokawa (d'après H. Maass), Seminar on Number Theory, Progr. Math, vol.8083, issue.12, pp.371-394, 1979.

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