In particular, the Hasse-Weil zeta functions of these varieties are computed at all places.doi:10.1007/978-3-8348-0352-8_2Don BlasiusViewegD.Blasius, Hilbert modular forms and the Ramanujan conjecture, Noncom- mutative geometry and number theory, 35-56, Aspects Math., E37, Vieweg, Wiesbaden...
Generalized modular forms including the weak Maass forms,the Ramanujan's Theta functions and the Tau function The modular forms are revisited from a geometric and an algebraic point of view leading to a geometric interpretation of the weak Maass forms connecting th... C Pierre - 《Eprint Arxiv...
Questions tagged [modular-forms] Ask Question A modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group. Learn more… Top users Synonyms 1...
In a recent paper, Kaneko and Zagier studied a sequence of modular forms Fk(z) which are solutions of a certain second order dieren tial equation. They studied the polynomials e Fk(j) = Y 2H= f i;!g (j j( ))ord (Fk); where ! = e2 i=3 and H= is the usual fundamental domai...
We show that the operator $U_p$ on the space of cuspidal modular forms of level $pN$ and weight two is semi-simple. It follows from this that the Hecke algebra acting on the space of weight two forms of level $M$ is reduced if $M$ is cube free. Assuming Tate's conjecture for ...
Metaplectic Ramanujan Conjecture Over Function Fields with Applications to Quadratic Forms. We formulate and prove the analog of the Ramanujan Conjectures for modular forms of half-integral weight subject to some ramification restriction in the se... Altuğ,Salim,Ali,... - 《Imrn International Mat...
Correction to: "On `-adic representations and congruences for coe卤cients of modular forms The work I shall describe in these lectures has two themes, a classical one going back to Ramanujan [8] and a modern one initiated by Serre [9] and Deligne [3]. To describe the classical theme,...
Statement of the Main Result 7. Distributions and admissible measures Notation Admissible measures of Amice-Vélu 7.1. Up–Operator and the method of canonical projection 8. Triple modular forms Eigenfunctions of Up and of Up∗. 9. Critical values of the L function L(f1 ⊗ f2 ⊗ f3, ...
s theory of theta functions; Eisenstein’s theory of elliptic functions (and let me plug another fantastic book: Weil’sElliptic Functions According to Eisenstein and Kronecker); Dedekind’s ηη-function; Ramanujan’s ττ-function; Dirichlet series and modular forms (Ch. 14); and “The ...
After this work was first released, Don Zagier communicated to us a proof of this assertion, and of the conjecture (5.54) below, based on the more elementary observation that\,\mathrm{Sym}\, F^{(0)}_n(\{c_i\})=2^{1-n}/nforneven, or 0 fornodd, irrespective of the value of ...