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References
Abromovich, M.: Handbook of Mathematical Functions. New York: Dover 1965
Barban, M.B.: Linnik's “large sieve” and a limit theorem for the class number of ideals of an imaginary quadratic field. Izv. Akad. Nauk SSSR Ser. Mat.26, 573–580 (1962)
Burgess, D.A.: On character sums andL-series, II. Proc. Lond. Math. Soc.13, 524–536 (1963)
Davenport, H.: Multiplicative Number Theory. Second Edition, pp. 105–106. Berlin-Heidelberg-New York: Springer 1980
Gauss, C.F.: Disquisitiones Arithmeticae. New Haven-London: Yale University Press 1966
Gauss, C.F.: Werke I, Zweiter Abdruck. Göttingen (1870), 369 and 466
Goldfeld, D., Hoffstein, J., Patterson, S.J.: On automorphic functions of half-integral weight with applications to elliptic curves. Number Theory Related to Fermat's Last Theorem, pp. 153–193. Boston: Birkhäuser 1982
Goldfeld, D., Viola, C.: Mean values ofL-functions associated to elliptic, Fermat and other curves at the center of the critical strip. J. Number Theory11, 305–320 (1979)
Goldfeld, D., Viola, C.: Some conjectures on elliptic curves over cyclotomic fields. Trans. Am. Math. Soc.276, 511–516 (1983)
Hardy, G., Riesz, M.: Dirichlet Series, p. 15, Cambridge: Cambridge Univ. Press (1952)
Hecke, E.: Lectures on the Theory of Algebraic Numbers. Berlin-Heidelberg-New York: Springer 1981
Jutila, M.: On the mean value ofL(1/3, χ) for real characters. Analysis1, 149–161 (1981)
Landau, E.: Elementary Number Theory. New York: Chelsea 1958
Lipschitz, R.: Sitzungsber. Akad. Berlin, pp. 174–185 (1865)
Mertens, F.: Über einige asymptotische Gesetze der Zahlentheorie. J. Math.77, 312–319 (1874)
Montgomery, H., Vaughn, R.C.: The distribution of squarefree numbers. Recent Prog. Analytic Number Theory1, 247–256 (Durham 1979). London-New York: Academic Press (1981)
Rankin, R.A.: Contributions to the theory of Ramanujan's function τ(n) and similar arithmetic functions. Proc. Cambridge Philos. Soc.35, 357–372 (1939)
Selberg, A.: Bemerkungen über eine Dirichletsche Reihe, die mit der Theorie der Modulformen nahe verbunden ist. Arch. Math. Naturrid43, 47–50 (1940)
Shimura, G.: On modular forms of half-integral weight. Ann. Math.97, 440–481 (1973)
Shimura, G.: On the holomorphy of certain Dirichlet series. Proc. Lond. Math. Soc.31, 79–96 (1975)
Shintani, T.: Zeta functions associated with the vector space of quadratic forms. J. Fac. Sci., Univ. Tokyo, Sect. IA22, 25–65 (1975)
Siegel, C.L.: The average measure of quadratic forms with given determinant and signature. Gesammelte Abhandlungen,II, pp. 473–491. Berlin-Heidelberg-New York: Springer (1966)
Stepanov, B.V.: On the mean value of thek th power of the number of classes for an imaginary quadratic field. Dokl. Akad. Nauk SSSR124, 984–986 (1959)
Takhtadzjan, L.A., Vinogradov, A.I.: On analogues of the Vinogradov-Gauss formula. Sov. Math., Dokl.22, 555–559 (1980)
Vinogradov, I.M.: Reprinted in his Selected Works. Izv. Rossiiskoi Akad. Nauk11, 1347 (1917). Izdat. Akad. Nauk SSSR, Moscow, p. 3, 1952
Vinogradov, I.M.: Reprinted in his Selected Works. Soobsc. Har'kov. Mat. Obsc.16, (1918); Izdat. Akad. Nauk SSSR, Moscow, p. 29, 1952
Vinogradov, I.M.: Reprinted in his Selected Works. Izv. Akad. Nauk SSSR, Ser. Mat.13, 97 (1949). Izdat. Akad. Nauk SSSR, Moscow, p. 366, 1952
Vinogradov, I.M.: Izv. Akad. Nauk SSSR, Ser. Mat.27, 957 (1963)
Walfisz, A., Weylsche Exponentialsummen in der neueren Zahlentheorie. Berlin: VEB Deutscher Verlag der Wissenschaften 1963
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Partially supported by NSF grant # DMS-8303621 and a grant from the Vaughn Foundation
Partially supported by NSF grant # MCS-8305527
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Goldfeld, D., Hoffstein, J. Eisenstein series of 1/2-integral weight and the mean value of real DirichletL-series. Invent Math 80, 185–208 (1985). https://doi.org/10.1007/BF01388603
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DOI: https://doi.org/10.1007/BF01388603