Geodesic
Sums of the additive divisor problem type
Zapiski Nauchnykh Seminarov POMI, Proceedings on number theory, Tome 322 (2005), pp. 239-250 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The inner product approach to the additive divisor problem with its cusp form analogues is surveyed, and a spectral summation formula for convolution sums involving Fourier coefficients of Maass forms is derived. An application to subconvexity estimates for Rankin–Selberg $L$-functions is announced. 
@article{ZNSL_2005_322_a15,
     author = {M. Jutila},
     title = {Sums of the additive divisor problem type},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {239--250},
     year = {2005},
     volume = {322},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_322_a15/}
}
TY  - JOUR
AU  - M. Jutila
TI  - Sums of the additive divisor problem type
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2005
SP  - 239
EP  - 250
VL  - 322
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2005_322_a15/
LA  - en
ID  - ZNSL_2005_322_a15
ER  - 
%0 Journal Article
%A M. Jutila
%T Sums of the additive divisor problem type
%J Zapiski Nauchnykh Seminarov POMI
%D 2005
%P 239-250
%V 322
%U http://geodesic.mathdoc.fr/item/ZNSL_2005_322_a15/
%G en
%F ZNSL_2005_322_a15
M. Jutila. Sums of the additive divisor problem type. Zapiski Nauchnykh Seminarov POMI, Proceedings on number theory, Tome 322 (2005), pp. 239-250. http://geodesic.mathdoc.fr/item/ZNSL_2005_322_a15/

[1] F. V. Atkinson, “The mean value of the zeta-function on the critical line”, Proc. London Math. Soc. (2), 47 (1941), 174–200 | DOI | MR

[2] V. Blomer, “Rankin–Selberg $L$-functions on the critical line” (to appear)

[3] A. Good, “Beiträge fur Theorie der Dirichletreihen, dir Spitzenformed zugeodnet sind”, J. Number Theory, 13 (1981), 18–65 | DOI | MR | Zbl

[4] A. Good, “The square mean of Dirichlet series associated with cusp forms”, Mathematika, 29 (1982), 278–295 | DOI | MR | Zbl

[5] M. Jutila, Advances in Number Theory, The proceedings of the third conference of the Canadian Number Theory Association, held at Queen's University (Kingston, Canada, August 18–24, 1991), eds. F. Q. Gouvêa, N. Yui, Clarendon Press, Oxford, 1993, 113–135 | MR | Zbl

[6] M. Jutila, “The additive divisor problem and its analogs for Fourier coefficients of cusp forms, I”, Math. Z., 223 (1996), 435–461 | MR | Zbl

[7] M. Jutila, “The additive divisor problem and its analogs for Fourier coefficients of cusp forms, II”, Math. Z., 225 (1997), 625–637 | DOI | MR | Zbl

[8] M. Jutila, “Mean Values of Dirichlet Series via Laplace Transforms”, Analytic Number Theory, ed. Y. Motohashi, Cambridge University Press, 1997, 169–207 | MR | Zbl

[9] M. Jutila, Y. Motohashi, “Mean value estimates for exponential sums and $L$-functions: a spectral theoretic approach”, J. Reine Angew. Math., 459 (1995), 61–87 | DOI | MR | Zbl

[10] M. Jutila, Y. Motohashi, “Uniform bound for Hecke $L$-functions” (to appear)

[11] N. N. Lebedev, Special Functions and their Applications, Dover, 1972 | MR

[12] Y. Motohashi, “The binary additive divisor problem”, Ann. Sci. École Norm. Sup. (4), 27 (1994), 529–572 | MR | Zbl

[13] Y. Motohashi, “The mean square of Hecke $L$-series attached to holomorphic cusp-forms”, RIMS Kyoto Univ. Kokyuroku, 886 (1994), 214–227 | MR | Zbl

[14] Y. Motohashi, Spectral Theory of the Riemann Zeta-Function, Cambridge University Press, 1997 | MR

[15] Y. Motohashi, “A note on the mean value of the zeta and $L$-functions, XIV”, Proc. Japan Acad. Ser. A Math. Sci, 80:4 (2004), 28–33 | DOI | MR | Zbl

[16] P. Sarnak, “Estimation of Rankin–Selberg $L$-functions and quantum unique ergodicity”, J. Functional Anal., 184 (2001), 419–453 | DOI | MR | Zbl

[17] A. Selberg, “On the estimation of Fourier coefficients of modular forms”, Proc. Symp. Pure Math., 8 (1965), 1–15 | MR | Zbl

[18] L. A. Takhtajan, A. I. Vinogradov, “The zeta-function of the additive divisor problem and the spectral decomposition of the automorphic Laplacian”, Zap. Nauchn. Sem. LOMI, 134, 1984, 84–116 | MR | Zbl