## Tables from this paper

## 14 Citations

### On the integrality of the Taylor coefficients of mirror maps

- Mathematics
- 2009

We show that the Taylor coefficients of the series ${\bf q}(z)=z\exp({\bf G}(z)/{\bf F}(z))$ are integers, where ${\bf F}(z)$ and ${\bf G}(z)+\log(z) {\bf F}(z)$ are specific solutions of certain…

### Congruences between extremal modular forms and theta series of special types modulo powers of 2 and 3

- Mathematics
- 2009

Heninger, Rains and Sloane proved that the nth root of the theta series of any extremal even unimodular lattice in Rn has integer coefficients if n is of the form 2i3j5k(i ≥ 3). Motivated by their…

### The partition-frequency enumeration matrix

- MathematicsThe Ramanujan Journal
- 2022

Abstract. We develop a calculus that gives an elementary approach to enumerate partition-like objects using an infinite upper-triangular number-theoretic matrix. We call this matrix the…

### N T ] 2 N ov 2 00 6 On Rationally Parametrized Modular Equations

- Mathematics
- 2008

The classical theory of elliptic modular equations is refor mulated and extended, and many new rationally parametrized modular equations are dis covered. Each arises in the context of a family of…

### 7 N ov 2 00 6 On Rationally Parametrized Modular Equations

- Mathematics
- 2008

The classical theory of elliptic modular equations is refor mulated and extended, and many new rationally parametrized modular equations are dis covered. Each arises in the context of a family of…

### On Rationally Parametrized Modular Equations

- Mathematics
- 2006

Many rationally parametrized elliptic modular equations are derived. Each comes from a family of elliptic curves attached to a genus-zero congruence subgroup $\Gamma_0(N)$, as an algebraic…

### Intégralité des coefficients de Taylor de racines d’applications miroir@@@Integrality of the Taylor coefficients of roots of mirror maps

- Mathematics
- 2012

We prove the integrality of the Taylor coefficients of roots of mirror maps at the origin. By mirror maps, we mean formal power series z.exp(G(z)/F(z)), where F(z) and G(z)+log(z)F(z) are particular…

### On Dwork's p-adic formal congruences theorem and hypergeometric mirror maps

- Mathematics
- 2013

Using Dwork's theory, we prove a broad generalisation of his famous p-adic formal congruences theorem. This enables us to prove certain p-adic congruences for the generalized hypergeometric series…

### Nonlinear differential equations satisfied by certain classical modular forms

- MathematicsManuscripta Mathematica
- 2010

A unified treatment is given of low-weight modular forms on Γ0(N), N = 2,3,4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of…

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