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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Showing 2008Show all

6 papers · 1 filter

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…