A common answer to question 1 is to mention the entries of Gauss's diary from 1814, including famously (but not restricted to) the last one, in which he studies some properties of biquadratic reciprocities and their links with the division of the lemniscate. Gauss understood these properties to derive from properties of Punktgitter (lattices of points) in the complex planes and his formulation is surprisingly close to the statement that (some) elliptic curves with CM are automorphic objects.

Though I am not sure that this is the best way to think about the work of Gauss himself (he himself seems to have been unsatisfied with his work and to have considered it of relatively low value compared to the latter approach of Einsenstein) and though it had no impact on mathematics at the time for the simple reason that it was kept private for over 80 years, it certainly counts as work done on "automorphic geometry" done in the early XIX° century.

A common answer to question 1 is to mention the entries of Gauss's diary from 1814, including famously (but not restricted to) the last one, in which he studies some properties of biquadratic reciprocity and their links with the division of the lemniscate. Gauss understood these properties to derive from properties of Punktgitter (lattices of points) in the complex planes and his formulation is surprisingly close to the statement that (some) elliptic curves with CM are automorphic objects.

Though I am not sure that this is the best way to think about the work of Gauss from a historical point of view (he himself seems to have been unsatisfied with this work and to have considered it of relatively low value compared to the latter approach of Einsenstein) and though these findings had no impact on mathematics at the time for the simple reason that they were kept private for over 80 years, it certainly counts as work in "automorphic geometry" done in the early XIX° century.

A common answer to question 1 is to mention the entries of Gauss's diary from 1814, including famously (but not restricted to) the last one, in which he studies some properties of biquadratic reciprocities and their links with the division of the lemniscate. Gauss understood these properties to derive from properties of Punktgitter (lattices of points) in the complex planes and is formulation is surprisingly close to the statement that (some) elliptic curves with CM are automorphic objects.

Though I am not sure that this is the best way to think about the work of Gauss himself (he himself seems to have been unsatisfied with his work and to have considered it of relatively low value compared to the latter approach of Einsenstein) and though it had no impact on mathematics at the time for the simple reason that it was kept private for over 80 years, it certainly counts as work done on "automorphic geometry" done in the early XIX° century.

A common answer to question 1 is to mention the entries of Gauss's diary from 1814, including famously (but not restricted to) the last one, in which he studies some properties of biquadratic reciprocities and their links with the division of the lemniscate. Gauss understood these properties to derive from properties of Punktgitter (lattices of points) in the complex planes and his formulation is surprisingly close to the statement that (some) elliptic curves with CM are automorphic objects.

Though I am not sure that this is the best way to think about the work of Gauss himself (he himself seems to have been unsatisfied with his work and to have considered it of relatively low value compared to the latter approach of Einsenstein) and though it had no impact on mathematics at the time for the simple reason that it was kept private for over 80 years, it certainly counts as work done on "automorphic geometry" done in the early XIX° century.