Baskar Balasubramanyam
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View article: Estimates of automorphic forms on $\mathrm{SU}(n,1)$
Estimates of automorphic forms on $\mathrm{SU}(n,1)$ Open
For $n\geq 2$, let $Γ\subset \mathrm{SU}((n,1),\mathcal{O}_{K})$ be a torsion-free, finite-index subgroup, where $\mathcal{O}_K$ denotes the ring of integers of a totally imaginary number field $K$ of degree $2$. Let $\mathbb{B}^n$ denote …
View article: A discrepancy result for Hilbert modular forms
A discrepancy result for Hilbert modular forms Open
Let $F $ be a totally real number field and $r=[F :\mathbb{Q}].$ Let $A_k(\mathfrak{N},ω) $ be the space of holomorphic Hilbert cusp forms with respect to $K_1(\mathfrak{N})$, weight $k=(k_1,\,...\,,k_r)$ with $k_j>2,$ for all $j$ and cent…
View article: Estimates of cusp forms for certain cocompact arithmetic subgroups
Estimates of cusp forms for certain cocompact arithmetic subgroups Open
In this article, we derive a sub convexity estimate of Hecke eigen cusp forms associated to certain cocompact arithmetic subgroups of SL(2,R). The main result can be considered as the holomorphic version of the estimate of Hecke eigen Maas…
View article: A $p$-adic adjoint $L$-function and the ramification locus of the Hilbert modular eigenvariety
A $p$-adic adjoint $L$-function and the ramification locus of the Hilbert modular eigenvariety Open
Let $F$ be a totally real field and $\mathscr{E}$ the middle-degree eigenvariety for Hilbert modular forms over $F$, constructed by Bergdall--Hansen. We study the ramification locus of $\mathscr{E}$ in relation to the $p$-adic properties o…
View article: p-adic adjoint L-function and ramification locus of the Hilbert eigenvariety
p-adic adjoint L-function and ramification locus of the Hilbert eigenvariety Open
Let $F$ be a totally real field. Let $\pi$ be a cuspidal cohomological automorphic representation for $\mathrm{GL}_2/F$. Let $L(s, \mathrm{Ad}^0, \pi)$ denote the adjoint $L$-function associated to $\pi$. The special values of this $L$-fun…
View article: Pair correlation statistics for Sato-Tate sequences
Pair correlation statistics for Sato-Tate sequences Open
We investigate the pair correlation statistics for sequences arising from Hecke eigenvalues with respect to spaces of primitive modular cusp forms. We derive the average pair correlation function of Hecke angles lying in small subintervals…
View article: Estimates of automorphic forms over quaternion algebras
Estimates of automorphic forms over quaternion algebras Open
In this article, using methods from geometric analysis and theory of heat kernels, we derive qualitative estimates of automorphic cusp forms defined over quaternion algebras. Using which, we prove an average version of the holomorphic QUE …
View article: p-adic Asai transfer
p-adic Asai transfer Open
Let $K/Q$ be a real quadratic field. Given an automorphic representation $π$ for $GL_{2}/K$, let $As^{\pm}(π)$ denote the plus/minus Asai transfer of $π$ to an automorphic representation for $GL_{4}/Q$. In this paper, we construct a rigid …
View article: Special values of adjoint L-functions and congruences for automorphic forms on GL(n) over a number field
Special values of adjoint L-functions and congruences for automorphic forms on GL(n) over a number field Open
We prove an integrality result for the value at $s=1$ of the adjoint $L$-function associated to a cohomological cuspidal automorphic representation on ${\rm GL}(n)$ over any number field. We then show that primes (outside an exceptional se…