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2-adic and 3-adic part of class numbers and properties of central values of L-functions
5-dissections and sign patterns of Ramanujan's parameter and its companion
In 1998, Michael Hirschhorn discovered the 5-dissection formulas of the Rogers-Ramanujan continued fraction and its reciprocal. We obtain the 5-dissections for functions and , which are essentially Ramanujan’s parameter and its companion. Additionally, 5-dissections of the reciprocals of these two functions are derived. These 5-dissection formulas imply that the coefficients in their series expansions have periodic sign patterns with few exceptions.
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 certain Dirichlet series attached to Siegel modular forms of degree two.
A characterization of integral elliptic automorphic forms
A class of conjectured series representations for .
A Classical Diophantine Problem and Modular Forms of Weight 3/2.
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 congruence for the coefficients in a series for π
A constructive approach to p-adic deformations of arithmetic homology
A converse theorem for second-order modular forms of level N
A correspondence for the generalized Hecke algebra of the metaplectic cover , -adic.
A cubic analogue of the theta series.
A cubic analogue of the theta series. II.
A Cuspidal Class Number Formula for the Modular Curves X1(N).
A decomposition of the space of higher order modular cusp forms
A decomposition theorem for Jacobi forms.