Amod Agashe

activity

20012026

most citedA visible factor of the special L-value

3 citations · 10 across the 14 of their papers we have counts for

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14 papers · 1 filter

math.NT2026

The index of a certain quotient of the Hecke algebra in its normalization

Amod Agashe

Let $Γ$ be a congruence subgroup of $S L_{2} (Z)$ , and let $f$ be a normalized eigenform of weight $k$ on $Γ$ . Let $K$ denote the number field generated over $Q$ by the Fourier coeffic…

math.NT2025

Reducibility and rational torsion in modular abelian varieties

Amod Agashe, Matthew Winters

Let N be a square-free positive integer and let f be a newform of weight 2 on Γ_0(N). Let A denote the abelian subvariety of J_0(N) associated to f and let m be a maximal ideal of…

math.NT2015

A generalization of Kronecker's first limit formula to GL(n)

Amod Agashe

Kronecker's first limit formula gives the polar and constant terms of the Laurent series expansion of the Eisenstein series for SL(2,Z) at s=1. In this article, we generalize the f…

math.NT2013

Darmon points on elliptic curves over totally real fields

Amod Agashe, Mak Trifkovic

We show how to construct Darmon points on elliptic curves over totally real fields.

math.NT2012★ 1 cited

Constructing non-trivial elements of the Shafarevich-Tate group of an Abelian Variety over a Number Field

Amod Agashe, Saikat Biswas

The second part of the Birch and Swinnerton-Dyer (BSD) conjecture gives a conjectural formula for the order of the Shafarevich-Tate group of an elliptic curve in terms of other com…

math.NT2009★ 2 cited

Visibility and the Birch and Swinnerton-Dyer conjecture for analytic rank zero

Amod Agashe

Let $E$ be an optimal elliptic curve over $\Q$ of conductor $N$ having analytic rank zero, i.e., such that the $L$ -function $L_{E} (s)$ of $E$ does not vanish at $s = 1$ . Suppose there…

math.NT2009★ 1 cited

Mod-p reducibility, the torsion subgroup, and the Shafarevich-Tate group

Amod Agashe

Let $E$ be an optimal elliptic curve over $\Q$ of prime conductor $N$ . We show that if for an odd prime $p$ , the mod $p$ representation associated to $E$ is reducible (in particula…

math.NT2008

Rational torsion in elliptic curves and the cuspidal subgroup

Amod Agashe

Let $A$ be an elliptic curve over $\Q$ of square free conductor $N$ . We prove that if $A$ has a rational torsion point of prime order $r$ such that $r$ does not divide $6 N$ , then $…

math.NT2008★ 1 cited

A visible factor for analytic rank one

Amod Agashe

Let $E$ be an optimal elliptic curve of conductor $N$ , such that the $L$ -function of $E$ vanishes to order one at $s = 1$ . Let $K$ be a quadratic imaginary field in which all the pri…

math.NT2008

Visibility and the Birch and Swinnerton-Dyer conjecture for analytic rank one

Amod Agashe

Let $E$ be an optimal elliptic curve over $\Q$ of conductor $N$ having analytic rank one, i.e., such that the $L$ -function $L_{E} (s)$ of $E$ vanishes to order one at $s = 1$ . Let $K$ b…

math.NT2008★ 3 cited

A visible factor of the special L-value

Amod Agashe

Let~ $A$ be a quotient of $J_{0} (N)$ associated to a newform $f$ such that the special $L$ -value of $A$ (at $s = 1$ ) is non-zero. We give a formula for the ratio of the special $L$ -valu…

math.NT2008

Squareness in the special L-value and special L-values of twists

Amod Agashe

Let N be a prime and let A be a quotient of J_0(N) over Q associated to a newform such that the special L-value of A (at s=1) is non-zero. Suppose that the algebraic part of the sp…

math.NT2008★ 1 cited

The Modular number, Congruence number, and Multiplicity One

Amod Agashe

Let N be a positive integer and let f be a newform of weight 2 on Γ_0(N). In earlier joint work with K. Ribet and W. Stein, we introduced the notions of the modular number and the…

math.NT2001★ 1 cited

Constructing elliptic curves with a known number of points over a prime field

Amod Agashe, Kristin Lauter, Ramarathnam Venkatesan

Elliptic curves with a known number of points over a given prime field with n elements are often needed for use in cryptography. In the context of primality proving, Atkin and Mora…