# Some applications of large sieve in Riemann surfaces

Acta Arithmetica (1996)

- Volume: 77, Issue: 4, page 315-337
- ISSN: 0065-1036

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topFernando Chamizo. "Some applications of large sieve in Riemann surfaces." Acta Arithmetica 77.4 (1996): 315-337. <http://eudml.org/doc/206922>.

@article{FernandoChamizo1996,

author = {Fernando Chamizo},

journal = {Acta Arithmetica},

keywords = {spectral theory of automorphic forms; Maass cusps forms; Hecke operators; pretrace formula; large sieve; Riemann surface; hyperbolic circle problem; Fuchsian groups; sum of two squares; spectral theory; large sieve inequality; compact manifolds},

language = {eng},

number = {4},

pages = {315-337},

title = {Some applications of large sieve in Riemann surfaces},

url = {http://eudml.org/doc/206922},

volume = {77},

year = {1996},

}

TY - JOUR

AU - Fernando Chamizo

TI - Some applications of large sieve in Riemann surfaces

JO - Acta Arithmetica

PY - 1996

VL - 77

IS - 4

SP - 315

EP - 337

LA - eng

KW - spectral theory of automorphic forms; Maass cusps forms; Hecke operators; pretrace formula; large sieve; Riemann surface; hyperbolic circle problem; Fuchsian groups; sum of two squares; spectral theory; large sieve inequality; compact manifolds

UR - http://eudml.org/doc/206922

ER -

## References

top- [Ch] F. Chamizo, The large sieve in Riemann surfaces, this volume, 303-313
- [Du] W. Duke, Hyperbolic distribution problems and half-integral weight Maass forms, Invent. Math. 92 (1988), 73-90 Zbl0628.10029
- [Gr-Ry] I. S. Gradshteyn, I. M. Ryzhik, Tables of Integrals, Series and Products, 5th ed., A. Jeffrey (ed.), Academic Press, 1994
- [Gr] E. Grosswald, Representations of Integers as Sums of Squares, Springer, 1985 Zbl0574.10045
- [Ha] G. H. Hardy, The average of the functions P(x) and Δ(x), Proc. London Math. Soc. (2) 15 (1916), 192-213
- [Iw] H. Iwaniec, Introduction to the Spectral Theory of Automorphic Forms, Bibl. Rev. Mat. Iberoamericana, Madrid, 1995
- [Iw-Sa] H. Iwaniec, P. Sarnak, ${L}^{\infty}$-norms of eigenfunctions of arithmetic surfaces, Ann. of Math., to appear
- [Pa] S. J. Patterson, A lattice point problem in hyperbolic space, Mathematika 22 (1975), 81-88. (Corrigendum in 23 (1976), 27.) Zbl0308.10013
- [Ph-Ru] R. Phillips, Z. Rudnick, The circle problem in the hyperbolic plane, preprint Zbl0812.11035
- [Se] A. Selberg, On the estimation of Fourier coefficients of modular forms, in: Proc. Sympos. Pure Math. 8, Amer. Math. Soc., Providence, 1965, 1-5. Zbl0142.33903

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