The spectral mean value for linear forms in twisted coefficients of cusp forms

• Autorzy: Wenzhi Luo
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 70
• Numer: 4
• Strony: 377-391

Daty

wydano

1995

otrzymano

1993-02-17

poprawiono

1994-04-25

Twórcy

autor

Wenzhi Luo

• Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, California 94720, U.S.A.

Bibliografia

• [1] J.-M. Deshouillers and H. Iwaniec, Kloosterman sums and Fourier coefficients of cusp forms, Invent. Math. 70 (1982), 219-288.
• [2] J.-M. Deshouillers and H. Iwaniec, The non-vanishing of Rankin-Selberg zeta-functions at special points, in: The Selberg Trace Formula and Related Topics, Contemp. Math. 53, Amer. Math. Soc., Providence, R.I., 1986, 59-95.
• [3] I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Series and Products, Academic Press, New York and London, 1965.
• [4] D. A. Hejhal, The Selberg Trace Formula for PSL(2,R), Vol. 2, Lecture Notes in Math. 1001, Springer, 1983.
• [5] M. N. Huxley, The large sieve inequality for algebraic number fields. II: Means of moments of Hecke zeta-functions, Proc. London Math. Soc. (3) 21 (1970), 108-128.
• [6] H. Iwaniec, Fourier coefficients of cusp forms and the Riemann zeta-function, Séminaire de Théorie des Nombres, Bordeaux 1979-80.
• [7] M. Jutila, On spectral large sieve inequalities, preprint, 1991.
• [8] N. V. Kuznetsov, Petersson's conjecture for cusp forms of weight zero and Linnik's conjecture. Sums of Kloosterman sums, Mat. Sb. 111 (1980), 334-383 (in Russian).
• [9] W. Luo, On the non-vanishing of Rankin-Selberg L-functions, Duke Math. J. 69 (1993), 411-425.
• [10] H. L. Montgomery, Topics in Multiplicative Number Theory, Lecture Notes in Math. 227, Springer, 1971.
• [11] R. Phillips and P. Sarnak, On cusp forms for cofinite subgroups of PSL(2,R), Invent. Math. 80 (1985), 339-364.
• [12] R. A. Rankin, Contributions to the theory of Ramanujan's function τ(n) and similar arithmetic functions, Proc. Cambridge Philos. Soc. 35 (1939), 357-372.
• [13] A. Selberg, On the estimation of Fourier coefficients of modular forms, in: Proc. Sympos. Pure Math. 8, Amer. Math. Soc., Providence, R.I., 1965, 1-15.
• [14] A. Selberg, Collected Papers, Vol. 1, Springer, 1989, 626-674.
• [15] G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Princeton Univ. Press, 1971.
• [16] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford, 1951.
• [17] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge, 1944.