Cycle integrals of Maass forms of weight 0 and Fourier coefficients of Maass forms of weight 1/2

• Autorzy: A. Biró
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2000
• Tom: 94
• Numer: 2
• Strony: 103-152

Daty

wydano

2000

otrzymano

1997-09-15

poprawiono

1999-06-04

Twórcy

autor

A. Biró

• Mathematical Institute of the Hungarian Academy of Sciences, Realtanoda u. 13-15, H-1053 Budapest, Hungary

Bibliografia

• [A-L] Atkin, A. O. L., and Lehner, J., Hecke operators on $Γ_0(m)$, Math. Ann. 185 (1970), 134-160.
• [B] Biró, A., On a generalization of the Selberg trace formula, Acta Arith. 87 (1999), 319-338.
• [Da] Davenport, H., Multiplicative Number Theory, 2nd ed., Springer, Berlin, 1980.
• [Du] Duke, W., Hyperbolic distribution problems and half-integral weight Maass forms, Invent. Math. 92 (1988), 73-90.
• [G] J. Guo, On the positivity of the central critical values of automorphic L-functions for GL(2), Duke Math. J. 83 (1996), 157-190.
• [I1] Iwaniec, H., Introduction to the Spectral Theory of Automorphic Forms, Rev. Mat. Iberoamericana, 1995.
• [I2] Iwaniec, H., Topics in Classical Automorphic Forms, Lecture Notes, Rutgers University, 1995.
• [K-S] Katok, S., and Sarnak, P., Heegner points, cycles and Maass forms, Israel J. Math. 84 (1993), 193-227.
• [Ko1] Kohnen, W., Modular forms of half-integral weight on $Γ_0(4)$, Math. Ann. 248 (1985), 249-266.
• [Ko2] Kohnen, W., Fourier coefficients of modular forms of half-integral weight, ibid. 271 (1985), 237-268.
• [Ko3] Kohnen, W., Newforms of half-integral weight, J. Reine Angew. Math. 333 (1982), 32-72.
• [Ko-Z] Kohnen, W., and Zagier, D., Values of L-series of modular forms at the center of the critical strip, Invent. Math. 64 (1981), 175-198.
• [K] Kuznetsov, N. V., Petersson's conjecture for cusp forms of weight 0 and Linnik's conjecture. Sums of Kloosterman sums, Mat. Sb. 111 (1980), 334-383 (in Russian).
• [La] Landau, E., Vorlesungen über Zahlentheorie, 3 vol., Hirzel, Leipzig, 1927.
• [Le] Lebedev, N. N., Special Functions and their Applications, 2nd ed., Moscow, 1963.
• [M] Maass, H., Über die räumliche Verteilung der Punkte in Gittern mit indefiniter Metrik, Math. Ann. 138 (1959), 287-315.
• [M-O] Magnus, O., and Oberbettinger, F., Formulas and Theorems for the Functions of Mathematical Physics, Springer, Berlin, 1966.
• [N] Niwa, S., Modular forms of half-integral weight and the integral of certain theta functions, Nagoya Math. J. 56 (1974), 147-161.
• [P] Proskurin, N. V., General Kloosterman sums, preprint LOMI R-3-80, Akad. Nauk SSSR Mat. Inst. Leningr. Otd. (1980) (in Russian), MR 82E 10040.
• [P-Sz] Pólya, G., and Szegö, G., Problems and Theorems in Analysis, Vol. 1, Springer, Berlin, 1972.
• [Shim] Shimura, G., On modular forms of half-integral weight, Ann. of Math. (2) 97 (1973), 440-481.
• [Shin] Shintani, T., On construction of holomorphic cusp forms of half-integral weight, Nagoya Math. J. 58 (1975), 83-126.
• [Wal] Waldspurger, J. L., Sur les coefficients de Fourier des formes modulaires de poids demi-entier, J. Math. Pures Appl. 60 (1981), 375-484.
• [W] Watson, G. N., A Treatise on the Theory of Bessel Functions, 2nd ed., Cambridge Univ. Press, 1952.