Explicit formulas for the Fourier coefficients of Jacobi and elliptic modular forms.
Extreme values of symmetric power L-functions at 1
Formules de trace et non-annulation de fonctions L automorphes au niveau
Fourier coefficients of Hilbert cusp forms associated with mixed Hilbert cusp forms.
Fourier coefficients of Jacobi forms over Cayley numbers.
In this paper we shall compute explicitly the Fourier coefficients of the Eisenstein seriesEk,m(z,w) = 1/2 ∑(c,d)=1 (cz + d)-k ∑t∈o exp {2πim((az + b/cz +d)N(t)) + σ(t,(w/cz +d) - (cN(w)/cz + d)}which is a Jacobi form of weight k and index m defined on H1 x CC, the product of the upper half-plane and Cayley numbers over the complex field C. The coefficient of e2πi(nz + σ(t,w)) with nm > N(t) has the form-2(k - 4)/Bk-4 ∏p SpHere Sp is an elementary factor which depends only on νp(m), νp(t),...
Fourier Coefficients of Modular Forms of Half-Integral Weight.
Fourier coefficients of modular forms of half-integral weight.
Fourier coefficients of real analytic cusp forms of arbitrary real weight
Fourier expansions of complex-valued Eisenstein series on finite upper half planes.
Gauss's ₂F₁ hypergeometric function and the congruent number elliptic curve
Generalized divisor problem for new forms of higher level
Suppose that is a primitive Hecke eigenform or a Mass cusp form for with normalized eigenvalues and let be a real number. We consider the sum and show that for every and . The same problem was considered for the case , that is for the full modular group in Lü (2012) and Kanemitsu et al. (2002). We consider the problem in a more general setting and obtain bounds which are better than those obtained by the classical result of Landau (1915) for . Since the result is valid for arbitrary...
Hecke Eigenforms of Degree Two: Dirichlet Series and Euler Products.
Heegner cycles, modular forms and jacobi forms
We give a geometric interpretation of an arithmetic rule to generate explicit formulas for the Fourier coefficients of elliptic modular forms and their associated Jacobi forms. We discuss applications of these formulas and derive as an example a criterion similar to Tunnel's criterion for a number to be a congruent number.
How to compute the coefficients of the elliptic modular function .
Identities for traces of singular moduli
Integral power sums of Hecke eigenvalues
Intersection numbers of cycles on locally symmetric spaces and Fourier coefficients of holomorphic modular forms in several complex variables
Kloosterman Sums and Fourier Coefficients of Cusp Forms.
Kloosterman sums in residue classes
We prove upper bounds for sums of Kloosterman sums against general arithmetic weight functions. In particular, we obtain power cancellation in sums of Kloosterman sums over arithmetic progressions, which is of square-root strength in any fixed primitive congruence class up to bounds towards the Ramanujan conjecture.
Maass operators and van der Pol-type identities for Ramanujan's tau function