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

 Access to full text

 Full (PDF)

1. [1] J.-M. Deshouillers and H. Iwaniec, Kloosterman sums and Fourier coefficients of cusp forms, Invent. Math. 70 (1982), 219-288. 
2. [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. [3] I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Series and Products, Academic Press, New York and London, 1965. 
4. [4] D. A. Hejhal, The Selberg Trace Formula for PSL(2,R), Vol. 2, Lecture Notes in Math. 1001, Springer, 1983. 
5. [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. Zbl0215.07303
6. [6] H. Iwaniec, Fourier coefficients of cusp forms and the Riemann zeta-function, Séminaire de Théorie des Nombres, Bordeaux 1979-80. 
7. [7] M. Jutila, On spectral large sieve inequalities, preprint, 1991. 
8. [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). Zbl0427.10016
9. [9] W. Luo, On the non-vanishing of Rankin-Selberg L-functions, Duke Math. J. 69 (1993), 411-425. Zbl0789.11032
10. [10] H. L. Montgomery, Topics in Multiplicative Number Theory, Lecture Notes in Math. 227, Springer, 1971. Zbl0216.03501
11. [11] R. Phillips and P. Sarnak, On cusp forms for cofinite subgroups of PSL(2,R), Invent. Math. 80 (1985), 339-364. Zbl0558.10017
12. [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. Zbl0021.39202
13. [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. Zbl0142.33903
14. [14] A. Selberg, Collected Papers, Vol. 1, Springer, 1989, 626-674. 
15. [15] G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Princeton Univ. Press, 1971. Zbl0221.10029
16. [16] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford, 1951. Zbl0042.07901
17. [17] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge, 1944. 

1. Fernando Chamizo, Sums of squares in $\mathbb{Z}\left[\sqrt{k}\right]$