References
Brubaker, B., Bump, D.: in preparation
Brubaker, B., Bump, D., Chinta, G., Friedberg, S., Hoffstein, J.: in preparation
Bump, D., Friedberg, S., Hoffstein, J.: On some applications of automorphic forms to number theory. Bull. Am. Math. Soc., New Ser. 33, 157–175 (1996)
Bump, D., Friedberg, S., Hoffstein, J.: Sums of twisted GL(3) automorphic L-functions. In: Contributions to automorphic forms, geometry, and number theory, pp.131–162. Baltimore, MD: Johns Hopkins University Press 2004
Diaconu, A., Goldfeld, D., Hoffstein, J.: Multiple Dirichlet series and moments of zeta and L-functions. Compos. Math. 139, 297–360 (2003)
Fisher, B., Friedberg, S.: Double Dirichlet series over function fields. Compos. Math. 140, 613–630 (2004)
Friedberg, S., Hoffstein, J.: Nonvanishing theorems for automorphic L-functions on GL(2). Ann. Math. (2) 142, 385–423 (1995)
Gauss, C.F.: Disquisitiones arithmeticae. Translated into English by Arthur A. Clarke. New Haven, Conn.: Yale University Press 1966
Goldfeld, D., Hoffstein, J.: Eisenstein series of \(\frac{1}{2}\)-integral weight and the mean value of real Dirichlet L-series. Invent. Math. 80, 185–208 (1985)
Goldfeld, D., Viola, C.: Mean values of L-functions associated to elliptic, Fermat and other curves at the centre of the critical strip. J. Number Theory 11, S. Chowla Anniversary Issue, 305–320 (1979)
Jutila, M.: On the mean value of \(L(\frac{1}{2},\,\chi)\) for real characters. Analysis 1, 149–161 (1981)
Lipschitz, R.: Sitzungsber. Akad. Berlin, pp. 174–185, 1865
Siegel, C.L.: The average measure of quadratic forms with given determinant and signature. Ann. Math. (2) 45, 667–685 (1944)
Siegel, C.L.: Die Funktionalgleichungen einiger Dirichletscher Reihen (German). Math. Z. 63, 363–373 (1956)
Takhtadzjan, L.A., Vinogradov, A.I.: On analogues of the Gauss-Vinogradov formula (Russian). Dokl. Akad. Nauk SSSR 254, 1298–1301 (1980). English translation: Soviet Math. Dokl. 22, 555–559 (1980)
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Chinta, G. Mean values of biquadratic zeta functions. Invent. math. 160, 145–163 (2005). https://doi.org/10.1007/s00222-004-0407-y
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DOI: https://doi.org/10.1007/s00222-004-0407-y