Inspired by work done for systems of polynomial exponential equations, we study systems of equations involving the modular j function. We show general cases in which these systems have solutions, and then we look at certain situations in which the modular Schanuel conjecture implies that these systems have generic solutions. An unconditional result in this direction is proven for certain polynomial equations on j with algebraic coefficients
Inspired by the idea of blurring the exponential function, we define blurred variants of the j-funct...
We define modular equations describing the l-torsion subgroups of the Jacobian of a hyperelliptic cu...
We prove some unconditional cases of the Existential Closedness problem for the modular j-function. ...
I give a model-theoretic setting for the modular j function and its derivatives. These structures, h...
In this paper we prove a functional transcendence statement for the j-function which is an analogue ...
Abstract. It is possible to compute j(τ) and its modular equations with no perception of its related...
We gave an algorithm to compute the modular equation <pn(X,j) of j(z) in [4]. Using the data accu...
International audienceThe aim of this paper is to give a higher dimensional equivalent of the classi...
We describe the construction of a new type of modular equation for Weber functions. These bear some ...
The thesis starts with two expository chapters. In the first one we discuss abelian varieties with p...
Sets of appropriately normalized eta quotients, that we call level n Weber functions, are defined, a...
Assuming Schanuel's conjecture, we prove that any polynomial–exponential equation in one variable mu...
The Fourier coefficients of powers of the Dedekind eta function can be studied simultaneously. The v...
We prove the Existential Closedness conjecture for the differential equation of the j-function and i...
We give explicit upper and lower bounds on the size of the coefficients of the modular polynomials $...
Inspired by the idea of blurring the exponential function, we define blurred variants of the j-funct...
We define modular equations describing the l-torsion subgroups of the Jacobian of a hyperelliptic cu...
We prove some unconditional cases of the Existential Closedness problem for the modular j-function. ...
I give a model-theoretic setting for the modular j function and its derivatives. These structures, h...
In this paper we prove a functional transcendence statement for the j-function which is an analogue ...
Abstract. It is possible to compute j(τ) and its modular equations with no perception of its related...
We gave an algorithm to compute the modular equation <pn(X,j) of j(z) in [4]. Using the data accu...
International audienceThe aim of this paper is to give a higher dimensional equivalent of the classi...
We describe the construction of a new type of modular equation for Weber functions. These bear some ...
The thesis starts with two expository chapters. In the first one we discuss abelian varieties with p...
Sets of appropriately normalized eta quotients, that we call level n Weber functions, are defined, a...
Assuming Schanuel's conjecture, we prove that any polynomial–exponential equation in one variable mu...
The Fourier coefficients of powers of the Dedekind eta function can be studied simultaneously. The v...
We prove the Existential Closedness conjecture for the differential equation of the j-function and i...
We give explicit upper and lower bounds on the size of the coefficients of the modular polynomials $...
Inspired by the idea of blurring the exponential function, we define blurred variants of the j-funct...
We define modular equations describing the l-torsion subgroups of the Jacobian of a hyperelliptic cu...
We prove some unconditional cases of the Existential Closedness problem for the modular j-function. ...
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