On the Fourier coefficients of modular forms
On the Fourier coefficients of modular forms. II.
On the Fourier coefficients of small positive powers of 0 ... .
On the Fourier expansions of Jacobi forms.
On the Fourier expansions of Jacobi forms of half-integral weight.
On the functional properties of Bessel zeta-functions
Zeta-functions associated with modified Bessel functions are introduced as ordinary Dirichlet series whose coefficients are J-Bessel and K-Bessel functions. Integral representations, transformation formulas, a power series expansion involving the Riemann zeta-function and a recurrence formula are given. The inverse Laplace transform of Weber's first exponential integral is the basic tool to derive the integral representations. As an application, we give a new proof of the Fourier series expansion...
On the fundamental periods of automorphic forms of arithmetic type.
On the generalized Fermat equation over totally real fields
In a recent paper, Freitas and Siksek proved an asymptotic version of Fermat’s Last Theorem for many totally real fields. We prove an extension of their result to generalized Fermat equations of the form , where A, B, C are odd integers belonging to a totally real field.
On the Generating Functions of Certain Eisenstein Series.
On the generation of the coefficient field of a newform by a single Hecke eigenvalue
Let be a non-CM newform of weight . Let be a subfield of the coefficient field of . We completely settle the question of the density of the set of primes such that the -th coefficient of generates the field . This density is determined by the inner twists of . As a particular case, we obtain that in the absence of nontrivial inner twists, the density is for equal to the whole coefficient field. We also present some new data on reducibility of Hecke polynomials, which suggest questions...
On the Geometry of a Siegel Modular Threefold.
On the Graded Ring of Hubert Modular Forms Associated with Q (|..5).
On the graded rings of modular forms
On the higher mean over arithmetic progressions of Fourier coefficients of cusp forms
Let be the nth normalized Fourier coefficient of a holomorphic or Maass cusp form f for SL(2,ℤ). We establish the asymptotic formula for the summatory function as x → ∞, where q grows with x in a definite way and j = 2,3,4.
On the higher power moments of cusp form coefficients over sums of two squares
Let be a normalized primitive holomorphic cusp form of even integral weight for the full modular group . Denote by the th normalized Fourier coefficient of . We are interested in the average behaviour of the sum for , where and is any fixed positive integer. In a similar manner, we also establish analogous results for the normalized coefficients of Dirichlet expansions of associated symmetric power -functions and Rankin-Selberg -functions.
On the Holomorphic Differential Forms of the Siegel Modular Variety II.
On the hybrid mean value of Cochrane sums and generalized Kloosterman sums
On the hybrid mean value of Dedekind sums and Hurwitz zeta-function
On the image of -adic Galois representations for abelian varieties of type I and II.
On the image of -adic Galois representations
We explore the question of how big the image of a Galois representation attached to a -adic modular form with no complex multiplication is and show that for a “generic” set of -adic modular forms (normalized, ordinary eigenforms with no complex multiplication), all have a large image.