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Zeros on the critical line for Dirichlet series attached to certain cusp forms. (English) Zbl 0497.10018


MSC:

11F11 Holomorphic modular forms of integral weight
11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
11M35 Hurwitz and Lerch zeta functions
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References:

[1] Deligne, P.: La conjecture de Weil. I. Inst. Hautes Etudes Sci. Publ. Math.43, 273-307 (1974) · Zbl 0287.14001 · doi:10.1007/BF02684373
[2] Good, A.: Beiträge zur Theorie den Dirichletreihen, die Spitzenformen zugeordnet sind. J. Number Theory13, 18-65 (1981) · Zbl 0446.10022 · doi:10.1016/0022-314X(81)90028-7
[3] Hafner, J.L.: On the zeros of Dirichlets series associated with certain cusp forms. Bull. Am. Math. Soc.8, 340-342 (1983) · Zbl 0507.10025 · doi:10.1090/S0273-0979-1983-15111-X
[4] Hafner, J.L.: Explicit estimates in the arithmetic theory of cusp forms and Poincaré series. Math. Ann.264, 9-20 (1983) · Zbl 0507.10023 · doi:10.1007/BF01458047
[5] Hardy, G.H.: Note on Ramanujan’s function ?(n). Proc. Cambridge Phil. Soc.23, 675-680 (1927) · JFM 53.0150.01 · doi:10.1017/S0305004100011178
[6] hecke, E.: Über die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung. Math. Ann.112, 664-699 (1936) · Zbl 0014.01601 · doi:10.1007/BF01565437
[7] Hecke, E.: Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung. Math. Ann.114, 1-28 (1937) · Zbl 0015.40202 · doi:10.1007/BF01594160
[8] Lekkerkerker, C.G.: On the zeros of a class of Dirichlet series. Dissertation, Utrecht, 1955 · Zbl 1173.30301
[9] Mordell, L.J.: On Ramanujan’s empirical expansions of modular functions. Proc. Cambridge Phil. Soc.19, 117-124 (1920) · JFM 46.0605.01
[10] Moreno, C.J.: Prime number theorems for the coefficients of modular forms. Bull. Am. Math. Soc.78, 796-798 (1972) · Zbl 0274.10031 · doi:10.1090/S0002-9904-1972-13040-4
[11] Ogg, A.: Modular forms and Dirichlet series, New York: Benjamin 1969 · Zbl 0191.38101
[12] Rankin, R.A.: Contributions to the theory of Ramanujan’s function ?(n) and similar arithmetical functions. I, II. Proc. Cambridge Phil. Soc.35, 351-372 (1939) · JFM 65.0353.01 · doi:10.1017/S0305004100021095
[13] Selberg, A.: On the zeros of Riemann’s zeta-function. Skr. Norske. Vid.-Akad. Oslo I,10, 59 (1942)
[14] Titchmarsh, E.C.: The theory of the Riemann zeta function. London, New York: Oxford University Press (Clarendon) 1951 · Zbl 0042.07901
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