Sanoli Gun

ALGEBRAIC INDEPENDENCE OF VALUES OF MODULAR FORMS

We investigate values of modular forms with algebraic Fourier coefficients at algebraic arguments. As a consequence, we conclude about the nature of zeros of such modular forms. In particular, the singular values of modular forms (that is, values at CM points) are related to the recent work of Nesterenko. As an application, we deduce the transcendence of critical values of certain Hecke L-series. We also discuss how these investigations generalize to the case of quasi-modular forms with algebraic Fourier coefficients.

Transcendental Nature of Special Values of

In this paper, we study the non-vanishing and transcendence of special values of a varying class of L-functions and their derivatives. This allows us to investigate the transcendence of Petersson norms of certain weight one modular forms.

L

In this paper, we investigate a conjecture due to S. and P. Chowla and its generalization by Milnor. These are related to the delicate question of non-vanishing of L-functions associated to peri- odic functions at integers greater than 1. We report on some progress in relation to these conjectures. In a different vein, we link them to a conjecture of Zagier on multiple zeta values and also to linear independence of polylogarithms.

-Functions

Kohnen showed that the zeros of the Eisenstein series Ek in the standard fundamental domain other than i and ρ are transcendental. In this paper, we obtain similar results for a more general class of modular forms, using the earlier works of Kanou, Kohnen and the recent work of Getz.

On a Conjecture of Chowla and Milnor

Let

TRANSCENDENTAL ZEROS OF CERTAIN MODULAR FORMS

f

A Variant of Lehmer's Conjecture, II: The CM-case

be a normalized Hecke eigenform with rational integer Fourier coefficients. It is an interesting question to know how often an integer

On the Lacunarity of Two-Eta-Products

n

A note on special values of L -functions

has a factor common with the

Multiple Lerch Zeta Functions and an Idea of Ramanujan

n