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Seminaire de Théorie des Nombres de Bordeaux

Acta Arithmetica

### 5-dissections and sign patterns of Ramanujan's parameter and its companion

Czechoslovak Mathematical Journal

In 1998, Michael Hirschhorn discovered the 5-dissection formulas of the Rogers-Ramanujan continued fraction $R\left(q\right)$ and its reciprocal. We obtain the 5-dissections for functions $R\left(q\right)R{\left({q}^{2}\right)}^{2}$ and $R{\left(q\right)}^{2}/R\left({q}^{2}\right)$, 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.

Acta Arithmetica

### A canonical map between Hecke algebras

Bollettino dell'Unione Matematica Italiana

Sia $D$ un corpo di quaternioni indefinito su $\mathbf{Q}$ di discriminante $\mathrm{\Delta }$ e sia $\mathrm{\Gamma }$ il gruppo moltiplicativo degli elementi di norma 1 in un ordine di Eichler di $D$ di livello primo con $\mathrm{\Delta }$. Consideriamo lo spazio ${S}_{k}\left(\mathrm{\Gamma }\right)$ delle forme cuspidali di peso $k$ rispetto a $\mathrm{\Gamma }$ e la corrispondente algebra di Hecke ${\mathbf{H}}^{D}$. Utilizzando una versione della corrispondenza di Jacquet-Langlands tra rappresentazioni automorfe di ${D}^{×}$ e di $G{L}_{2}$, realizziamo ${\mathbf{H}}^{D}$ come quoziente dell'algebra di Hecke classica di livello $N\mathrm{\Delta }$. Questo risultato permette di...

### A certain Dirichlet series attached to Siegel modular forms of degree two.

Inventiones mathematicae

### A characterization of integral elliptic automorphic forms

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

### A class of conjectured series representations for $1/\pi$.

Experimental Mathematics

### A Classical Diophantine Problem and Modular Forms of Weight 3/2.

Inventiones mathematicae

### A combinatorial interpretation of Serre's conjecture on modular Galois representations

Annales de l’institut Fourier

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 $p$, by their counterparts in the theory of modular symbols.

### A condition for the rationality of certain elliptic modular forms over primes dividing the level

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let $f$ be a weight $k$ holomorphic automorphic form with respect to ${\mathrm{\Gamma }}_{0}\left(N\right)$. We prove a sufficient condition for the integrality of $f$ over primes dividing $N$. This condition is expressed in terms of the values at particular $CM$ curves of the forms obtained by iterated application of the weight $k$ Maaß operator to $f$ and extends previous results of the Author.

Acta Arithmetica

Acta Arithmetica

Acta Arithmetica

### A correspondence for the generalized Hecke algebra of the metaplectic cover $\overline{SL\left(2,F\right)}$, $F$$p$-adic.

The New York Journal of Mathematics [electronic only]

### A cubic analogue of the theta series.

Journal für die reine und angewandte Mathematik

### A cubic analogue of the theta series. II.

Journal für die reine und angewandte Mathematik

### A Cuspidal Class Number Formula for the Modular Curves X1(N).

Mathematische Annalen

Acta Arithmetica

### A decomposition theorem for Jacobi forms.

Mathematische Annalen

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