Narasimha Kumar

activity

20122022

most citedEquidistribution of signs for Hilbert modular forms of half-integral weight

7 citations · 25 across the 19 of their papers we have counts for

collaborators

20 papers

math.NT2022

On the solutions of $x^{p} + y^{p} = 2^{r} z^{p}$ , $x^{p} + y^{p} = z^{2}$ over totally real fields

Narasimha Kumar, Satyabrat Sahoo

In this article, we study the non-trivial primitive solutions of a certain type for the Diophantine equations $x^{p} + y^{p} = 2^{r} z^{p}$ and $x^{p} + y^{p} = z^{2}$ of prime exponent $p$ , $r \in \math…

math.NT2021★ 3 cited

The structure of Drinfeld modular forms of level $Γ_{0} (T)$ and applications

Tarun Dalal, Narasimha Kumar

In this article, we describe the structure of the $R$ -algebra of Drinfeld modular forms $M (Γ_{0} (T))_{R}$ (resp., $M^{0} (Γ_{0} (T))_{R}$ ) of level $Γ_{0} (T)$ and the structure of mod-$\p$ reduc…

math.NT2021★ 2 cited

Notes on Atkin-Lehner theory for Drinfeld modular forms

Tarun Dalal, Narasimha Kumar

In this article, we settle a part of the Conjecture by Bandini and Valentino (\cite{BV19a}) for $S_{k, l} (Γ_{0} (T))$ when $dim S_{k, l} (GL_{2} (A)) \leq 2$ . Then, we fra…

math.NT2021

On Congruences and Linear relations for Drinfeld modular forms of level $Γ_{0} (T)$ , arbitrary type

Tarun Dalal, Narasimha Kumar

In \cite{Cho09}, Choi studied congruences of coefficients (modulo $T^{q} - T$ ) for Drinfeld modular forms of level $Γ_{0} (T)$ , trivial type and the linear relations between the initial c…

math.NT2021

Cuspidal subgroups associated with non-rational Eisenstein maximal ideals

Debargha Banerjee, Narasimha Kumar, Dipramit Majumdar

In this paper, we are interested in the generalization of Ramanujan-like Eisenstein congruences (congruences between cusp forms and Eisenstein series) for congruence subgroups of t…

math.NT2021

On generation of the coefficient field of a primitive Hilbert modular form by a single Fourier coefficient

Narasimha Kumar, Satyabrat Sahoo

For a primitive Hilbert modular form $f$ over $F$ of weight $k$ , under certain assumptions on image of $ρ ˉ_{f, λ}$ , we calculate the Dirichlet density of primes $p$ fo…

math.NT2020★ 5 cited

On mod $p$ congruences for Drinfeld modular forms of level $pm$

Tarun Dalal, Narasimha Kumar

In~\cite{CS04}, Calegari and Stein studied the congruences between classical cusp forms $S_{k} (Γ_{0} (p))$ of prime level and made several conjectures about them. In~\cite{AB07} (resp.,…

math.NT2020

On non-vanishing of the Fourier coefficients of primitive forms

Tarun Dalal, Narasimha Kumar

In this semi-expository article, we discuss about the non-vanishing of the Fourier coefficients of primitive forms. Also, we shall make a note of a discrepancy in the statement of…

math.NT2018

A generalization of Mazur's theorem (Ogg's conjecture) for number fields

Debargha Banerjee, Narasimha Kumar, Dipramit Majumdar

In this article, we prove a generalization of a theorem (Ogg's conjecture) due to Bary Mazur for arbitrary $N \in N$ and for {\it number fields}. The main new observation is a modi…

math.NT2018

On non-vanishing and sign changes of the Fourier coefficients of Hilbert cusp forms

Narasimha Kumar, Tarun Dalal

In this article, we study (simultaneous) non-vanishing, (simultaneous) sign changes of Fourier coefficients of (two) Hilbert cusp forms, respectively.

math.NT2018★ 1 cited

Simultaneous behaviour of the Fourier coefficients of two Hilbert modular cusp forms

Surjeet Kaushik, Narasimha Kumar

In this article, we study the simultaneous sign changes of the Fourier coefficients of two Hilbert cusp forms of different integral weights. We also study the simultaneous non-vani…

math.NT2017

A variant of multiplicity one theorems for half-integral weight modular forms

Narasimha Kumar

We show that signs of Fourier coefficients, on certain sub-families, determine the half-integral weight cuspidal eigenform uniquely, up to a positive constant. We also study sign c…

math.NT2017★ 7 cited

Equidistribution of signs for Hilbert modular forms of half-integral weight

Surjeet Kaushik, Narasimha Kumar, Naomi Tanabe

We prove an equidistribution of signs for the Fourier coefficients of Hilbert modular forms of half-integral weight. Our study focuses on certain subfamilies of coefficients that a…

math.NT2016★ 1 cited

On the gaps between non-zero Fourier coefficients of eigenforms with CM

Surjeet Kaushik, Narasimha Kumar

Suppose $E$ is an elliptic curve over $Q$ of conductor $N$ with complex multiplication (CM) by $Q (i)$ , and $f_{E}$ is the corresponding cuspidal Hecke eigenform in…

math.NT2016★ 2 cited

On the gaps between non-zero Fourier coefficients of cusp forms of higher weight

Narasimha Kumar

We show that if a modular cuspidal eigenform $f$ of weight $2 k$ is $2$ -adically close to an elliptic curve $E / Q$ , which has a cyclic rational $4$ -isogeny, then $n$ -th Four…

math.NT2015

A 2-adic control theorem for modular curves

Narasimha Kumar

We study the behaviour of ordinary parts of the homology modules of modular curves, associated to a decreasing sequence of congruence subgroups $Γ_{1} (N 2^{r})$ for $r \geq 2$ , and prov…

math.NT2013

Remarks on q-exponents of generalized modular functions

Narasimha Kumar

In this note, we prove multiplicity one theorems for generalized modular functions (GMF), in terms of their q-exponents, and make a general statement about the nature of values tha…

math.NT2013★ 4 cited

A Note on the Fourier coefficients of half-integral weight modular forms

Narasimha Kumar, Soma Purkait

In this note, we show that the algebraicity of the Fourier coefficients of half-integral weight modular forms can be determined by checking the algebraicity of the first few of the…

math.NT2013

A Note on Fourier-Jacobi coefficients of Siegel modular forms

Sanoli Gun, Narasimha Kumar

Let F be a Siegel cusp form of weight k and genus n>1 with Fourier-Jacobi coefficients f_m. In this article, we estimate the growth of the Petersson norms of f_m, where m runs over…

math.NT2012

On sign changes of q-exponents of generalized modular functions

Narasimha Kumar

Let f be a generalized modular function of weight 0 of level N such that its q-exponents c(n)(n>0) are all real, and div(f) is zero. In this note, we show the equidistribution of s…

On the solutions of xp+yp=2rzp, xp+yp=z2 over totally real fields

The structure of Drinfeld modular forms of level Γ0​(T) and applications

Notes on Atkin-Lehner theory for Drinfeld modular forms

On Congruences and Linear relations for Drinfeld modular forms of level Γ0​(T), arbitrary type

Cuspidal subgroups associated with non-rational Eisenstein maximal ideals

On generation of the coefficient field of a primitive Hilbert modular form by a single Fourier coefficient

On mod p congruences for Drinfeld modular forms of level pm

On non-vanishing of the Fourier coefficients of primitive forms

A generalization of Mazur's theorem (Ogg's conjecture) for number fields

On non-vanishing and sign changes of the Fourier coefficients of Hilbert cusp forms

Simultaneous behaviour of the Fourier coefficients of two Hilbert modular cusp forms

A variant of multiplicity one theorems for half-integral weight modular forms

Equidistribution of signs for Hilbert modular forms of half-integral weight

On the gaps between non-zero Fourier coefficients of eigenforms with CM

On the gaps between non-zero Fourier coefficients of cusp forms of higher weight

A 2-adic control theorem for modular curves

Remarks on q-exponents of generalized modular functions

A Note on the Fourier coefficients of half-integral weight modular forms

A Note on Fourier-Jacobi coefficients of Siegel modular forms

On sign changes of q-exponents of generalized modular functions

On the solutions of $x^{p} + y^{p} = 2^{r} z^{p}$ , $x^{p} + y^{p} = z^{2}$ over totally real fields

The structure of Drinfeld modular forms of level $Γ_{0} (T)$ and applications

On Congruences and Linear relations for Drinfeld modular forms of level $Γ_{0} (T)$ , arbitrary type

On mod $p$ congruences for Drinfeld modular forms of level $pm$