A basis for the space of modular forms
A canonical map between Hecke algebras
Sia un corpo di quaternioni indefinito su di discriminante e sia il gruppo moltiplicativo degli elementi di norma 1 in un ordine di Eichler di di livello primo con . Consideriamo lo spazio delle forme cuspidali di peso rispetto a e la corrispondente algebra di Hecke . Utilizzando una versione della corrispondenza di Jacquet-Langlands tra rappresentazioni automorfe di e di , realizziamo come quoziente dell'algebra di Hecke classica di livello . Questo risultato permette di...
A characterization of integral elliptic automorphic forms
A combinatorial interpretation of Serre's conjecture on modular Galois representations
We state a conjecture concerning modular absolutely irreducible odd 2-dimensional representations of the absolute Galois group over finite fields which is purely combinatorial (without using modular forms) and proof that it is equivalent to Serre’s strong conjecture. The main idea is to replace modular forms with coefficients in a finite field of characteristic , by their counterparts in the theory of modular symbols.
A condition for the rationality of certain elliptic modular forms over primes dividing the level
Let be a weight holomorphic automorphic form with respect to . We prove a sufficient condition for the integrality of over primes dividing . This condition is expressed in terms of the values at particular curves of the forms obtained by iterated application of the weight Maaß operator to and extends previous results of the Author.
A decomposition of the space of higher order modular cusp forms
A larger GL 2 large sieve in the level aspect
In this paper we study the orthogonality of Fourier coefficients of holomorphic cusp forms in the sense of large sieve inequality. We investigate the family of GL 2 cusp forms modular with respect to the congruence subgroups Γ1(q), with additional averaging over the levels q ∼ Q. We obtain the orthogonality in the range N ≪ Q 2−δ for any δ > 0, where N is the length of linear forms in the large sieve.
A local large sieve inequality for cusp forms
We prove a large sieve type inequality for Maass forms and holomorphic cusp forms with level greater or equal to one and of integral or half-integral weight in short interval.
A negative result on the representation of modular forms by theta series.
A new multiple Dirichlet series induced by a higher-order form
A note on fields of definition
A relation between Fourier coefficients of holomorphic cusp forms and exponential sums
A relative trace formula proof of the Petersson trace formula
Action of Hecke Operator T(p) on Theta Series.
Affine Lie algebras and modular forms
All Congruent Numbers Less than 2000.
An analog of crank for a certain kind of partition function arising from the cubic continued fraction
An analytic function and iterated integrals
An application of the projections of automorphic forms
An infinite ferm in the universal deformation space of Galois representations.
I hope this article will be helpful to people who might want a quick overview of how modular representations fit into the theory of deformations of Galois representations. There is also a more specific aim: to sketch a construction of a point-set topological'' configuration (the image of an infinite fern'') which emerges from consideration of modular representations in the universal deformation space of all Galois representations. This is a configuration hinted previously, but now, thanks to some...