Sums of the kth divisor function of the ternary quadratic with prime variables

Yuetong Zhao1, Wei Zhai, Jinjiang Li
1China University of Mining and Technology

Tóm tắt

Từ khóa


Tài liệu tham khảo

Calderón, C., de Velasco, M.J.: On divisors of a quadratic form. Bol. Soc. Brasil. Mat. 31, 81–91 (2000)

Guo, R.T., Zhai, W.G.: Some problems about the ternary quadratic form $$m_1^2+m_2^2+m_3^2$$. Acta Arith. 156, 101–121 (2012)

Zhao, L.L.: The sum of divisors of a quadratic form. Acta Arith. 163, 161–177 (2014)

Sun, Q.F., Zhang, D.Y.: Sums of the triple divisor function over values of a ternary quadratic form. J. Number Theory 168, 215–246 (2016)

Kolesnik, G.: On the order of Dirichlet L-functions. Pac. J. Math. 82(2), 479–484 (1979)

Pan, C.D., Pan, C.B.: Fundamentals of Analytic Number Theory. Science Press, Beijing (1991). (in Chinese)

Meurman, T.: The mean twelfth power of Dirichlet L-functions on the critical line. Ann. Acad. Sci. Fenn. Ser. A I Math. Disser. 52, 1–44 (1984)

Ivić, A.: The Riemann Zeta-Function. Wiley, New York (1985)

Karatsuba, A.A.: Basic Analytic Number Theory, 2nd edn (Nathanson, B., Trans.). Springer, Berlin (1993)

Vaughan, R.C.: The Hardy–Littlewood Method, 2nd edn. Cambridge University Press, Cambridge (1997)

Pan, C.D., Pan, C.B.: Goldbach Conjecture. Science Press, Beijing (1981). ((in Chinese))

Zhang, D.Y., Wang, Y.N.: Ternary quadratic form with prime variables attached to Fourier coefficients of primitive holomorphic cusp form. J. Number Theory 176, 211–225 (2017)