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Transcendental values of certain Eichler integrals
We study the transcendence of certain Eichler integrals associated to Eisenstein series and more generally to modular forms using functional identities due to Ramanujan, Grosswald, Weil et al. TheExpand
On a Conjecture of Chowla and Milnor
Abstract 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 associatedExpand
Transcendence of the log gamma function and some discrete periods
Abstract We study transcendental values of the logarithm of the gamma function. For instance, we show that for any rational number x with 0 x 1 , the number log Γ ( x ) + log Γ ( 1 − x ) isExpand
  • S. Gun
  • Mathematics
  • 1 December 2006
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 ofExpand
Linear independence of digamma function and a variant of a conjecture of Rohrlich
Abstract Let ψ ( x ) denote the digamma function. We study the linear independence of ψ ( x ) at rational arguments over algebraic number fields. We also formulate a variant of a conjecture ofExpand
Divisors of Fourier coefficients of modular forms
Let $d(n)$ denote the number of divisors of $n$. In this paper, we study the average value of $d(a(p))$, where $p$ is a prime and $a(p)$ is the $p$-th Fourier coefficient of a normalized HeckeExpand
Simultaneous sign change of Fourier-coefficients of two cusp forms
We consider the simultaneous sign change of Fourier coefficients of two modular forms with real Fourier coefficients. In an earlier work, the second author with Sengupta proved that two cusp forms ofExpand
Random ordering in modulus of consecutive Hecke eigenvalues of primitive forms
Let $\unicode[STIX]{x1D70F}(\cdot )$ be the classical Ramanujan $\unicode[STIX]{x1D70F}$ -function and let $k$ be a positive integer such that $\unicode[STIX]{x1D70F}(n)\neq 0$ for $1\leqslantExpand
A note on special values of $L$-functions
In this paper, we link the nature of special values of certain Dirichlet L-functions to those of multiple gamma values.
The first simultaneous sign change and non-vanishing of Hecke eigenvalues of newforms
Let $f$ and $g$ be two distinct newforms with weights $k_1, k_2 \ge 2$ and square-free levels $N_1, N_2 \ge 1$ respectively and which are normalized Hecke eigenforms. Further, for $n\ge 1$, let $Expand