#### Hall 123

#### On arithmetic nature of values of theta-constants

#### Veekesh Kumar

##### IMSc

*In 2007 Y. V. Nesterenko proved that for \tau_1, \tau_2 in the complex upper half plane such that {1,\tau_1, \tau_2} are Q-linearly independent, at least one of the quotients*

theta_2(\tau_1) / theta_3(\tau_1), theta_2(\tau_2) / theta_3(\tau_1), theta_3(\tau_2) / theta_3(\tau_1)

is transcendental. In this talk, I will discuss the proof of this result and some interesting consequences of this theorem. We will also see some future problems in this direction.

Note: This is an in-person seminar. Please follow all covid protocols.

Done