PUJAHARI, SUDHIR(IISER PuneDept. of Mathematics, 2016-11)
In the thesis, we have studied effective distribution of gaps between elements of one or more than one sequences. We also have studied a multiplicity one kind theorem for cusp forms.
This thesis presents an exposition of a result of Serre about the asymptotic distribution of
eigenvalues of families of regular graphs. This result is part of a paper published by Serre
in 1997 titled \the equidistribution ...
A famous conjecture of Sato and Tate (now a celebrated theorem of Taylor et
al) predicts that the normalised p-th Fourier coeffcients of a non-CM Hecke
eigenform follow the Sato-Tate distribution as we vary the primes ...
We give three results concerning the distribution of eigenvalues of Hecke operators acting on spaces of modular cusp forms of weight k with respect to Γ_0(N) by attaching some weights to them. These results extend some ...
An elliptic curve $E$ over a field $\mathbb{F}$ can be defined by the equation $$y^2 = x^3 + ax+ b,$$ where $a, \, b \in \mathbb{F}.$
For any $r \geq 1$, let $a_E{(p^r)}$ denote the trace of the Frobenius endomorphism ...
Let F be a totally real number field, r = [F : Q], and N be an
integral ideal. Let Ak(N, ω) be the space of holomorphic Hilbert cusp forms
with respect to K1(N), weight k = (k1, ..., kr) with kj > 2, kj even for all
j ...
In [BS19], Balasubramanyam and Sinha derived the first moment of the pair correlation function for Hecke angles lying in small subintervals of [0, 1], as one averages over large families of Hecke newforms of weight k with ...