A trace formula for the scalar product of Hecke series and its applications View Full Text


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Article Info

DATE

1998-03

AUTHORS

V. A. Bykovskii

ABSTRACT

A trace formula expressing the mean values of the form (k=2,3,...) via certain arithmetic means on the group Г0(N1) is proved. Here the sum is taken over a normalized orthogonal basis in the space of holomorphic cusp forms of weight 2k with respect to Г0(N1). By Hf(x)(s) we denote the Hecke series of the form f, twisted with the primitive character χ (mod N2), and λf(d), (d, N1N2)=1, are the eigenvalues of the Hecke operators. The trace formula is used for obtaining the estimate for the newform f for all ε>0, l=0,1,2,.... This improves the known result (Duke-Friedlander-Iwaniec, 1993) with upper bound (1+|t|)2N21/2−1/22+ε on the right-hand side. As a corollary, we obtain the estimate for the Fourier coefficients of holomorphic cusp forms of weight k+1/2, which improves Iwaniec' result (1987) with exponent 1/4–1/28+ε. Bibliography: 25 titles. More... »

PAGES

915-932

References to SciGraph publications

  • 1974-12. La conjecture de Weil. I in PUBLICATIONS MATHÉMATIQUES DE L'IHÉS
  • 1980. Multiplicative Number Theory in NONE
  • 1987-03. Heegner points and derivatives ofL-series. II in MATHEMATISCHE ANNALEN
  • 1978-06. Hybrid bounds for DirichletL-functions in INVENTIONES MATHEMATICAE
  • 1985-04. Fourier coefficients of modular forms of half-integral weight in MATHEMATISCHE ANNALEN
  • 1993-12. Bounds for automorphicL-functions in INVENTIONES MATHEMATICAE
  • 1973. Formes Modulaires et Representations De GL(2) in MODULAR FUNCTIONS OF ONE VARIABLE II
  • 1986-06. Heegner points and derivatives ofL-series in INVENTIONES MATHEMATICAE
  • 1987-06. Fourier coefficients of modular forms of half-integral weight in INVENTIONES MATHEMATICAE
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/bf02358528

    DOI

    http://dx.doi.org/10.1007/bf02358528

    DIMENSIONS

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