Let f be a primitive positive integral binary quadratic form of discriminant −D, and let rf (n) be the number of representations of n by f up to automorphisms of f . In this article, we give… (More)

Let F = (F1, . . . , Fm) be an m-tuple of primitive positive binary quadratic forms and let UF(x) be the number of integers not exceeding x that can be represented simultaneously by all the forms Fj… (More)

We prove an upper bound for the L4-norm and for the L2-norm restricted to the vertical geodesic of a holomorphic Hecke cusp form f of large weight k. The method is based on Watson’s formula and… (More)

Let K be a totally real number field, π an irreducible cuspidal representation of GL2(K)\GL2(AK) with unitary central character, and χ a Hecke character of conductor q. Then L(1/2, π ⊗ χ) (Nq) 2− 8… (More)

Let q be a large prime and χ the quadratic character modulo q. Let φ be a self-dual cuspidal Hecke eigenform for SL(3,Z), and f a Hecke-Maaß cusp form for Γ0(q) ⊆ SL2(Z). We consider the twisted… (More)

For two real characters ψ, ψ ′ of conductor dividing 8 define Z(s, w; ψ, ψ ′) := ζ 2 (2s + 2w − 1) X d odd L 2 (s, χ d ψ)ψ ′ (d) d w where χ d = " d. " and the subscript 2 denotes that the Euler… (More)

Let g be a cuspidal newform (holomorphic or Maass) of arbitrary level and nebentypus, w a primitive character of conductor q, and s a point on the critical line <s 1⁄4 12 . It is proved that Lðgn w;… (More)

Let f be a primitive (holomorphic or Maaß) cusp form of level q and nontrivial nebentypus. Then for Re s = 1 2 the associated L-function satisfies L(f, s) q 1 4− 1 1889 , where the implied constant… (More)

Let f(z) = P n a(n)n e(nz) ∈ Sk(N, χ) be a cusp form for Γ0(N), weight k > 4 and character χ. Let q(x) = x + sx + t ∈ Z[x] be a quadratic polynomial. It is shown that

We develop a fairly explicit Kuznetsov formula on GL(3) and discuss the analytic behavior of the test functions on both sides. Applications to Weyl's law, exceptional eigenvalues, a large sieve and… (More)