Publications Influence

Share This Author

## Yoshida lifts and Selmer groups

- Siegfried Bocherer, N. Dummigan, R. Schulze-Pillot
- Mathematics
- 28 December 2010

Let f and g, of weights k 0 > k 2, be normalised newforms for 0(N), for square-free N > 1, such that, for each Atkin-Lehner involution, the eigenvalues of f and g are equal. Let j ' be a large prime… Expand

## Symmetric Square L-Functions and Shafarevich-Tate Groups

- N. Dummigan
- MathematicsExp. Math.
- 1 January 2001

We use Zagier's method to compute the critical values of the symmetric square L-functions of six cuspidal eigenforms of level one with rational coefficients. According to the Bloch-Kato conjecture,… Expand

## The representation of integers by binary additive forms

- M. Bennett, N. Dummigan, T. Wooley
- MathematicsCompositio Mathematica
- 1 March 1998

Let a, b and n be integers with ≥ 3. We show that, in the sense of natural density, almost all integers represented by the binary form axn − byn are thus represented essentially uniquely. By… Expand

## Congruences of modular forms and Selmer groups

- N. Dummigan
- Mathematics
- 2001

We show that the congruence modulo 11 between the normalized cusp form ∆ of weight 12 and the normalized cusp form of weight 2 and level 11 ‘descends’ to a congruence between forms of weights 13/2… Expand

## SOME SIEGEL MODULAR STANDARD L-VALUES, AND SHAFAREVICH-TATE GROUPS

- N. Dummigan, T. Ibukiyama, H. Katsurada
- Mathematics
- 23 October 2009

## EULER FACTORS AND LOCAL ROOT NUMBERS FOR SYMMETRIC POWERS OF ELLIPTIC CURVES

- N. Dummigan, Phil Martin, M. Watkins
- Mathematics
- 2009

For any elliptic curve E over a number field, there is, for each n � 1, a symmetric n th -power L-function, defined by an Euler product, and conjecturally having a meromorphic continuation and… Expand

## SYMMETRIC SQUARE L-FUNCTIONS AND SHAFAREVICH–TATE GROUPS, II

- N. Dummigan
- Mathematics
- 1 November 2009

We re-examine some critical values of symmetric square L-functions for cusp forms of level one. We construct some more of the elements of large prime order in Shafarevich–Tate groups, demanded by the… Expand

## LEVEL-LOWERING FOR HIGHER CONGRUENCES OF MODULAR FORMS

- N. Dummigan
- Mathematics
- 2014

We prove a level-lowering result for modular forms mod n , and use it to calculate some Tamagawa factors.

## Quinary forms and paramodular forms

- N. Dummigan, Ariel Pacetti, Gustavo Rama, Gonzalo Tornar'ia
- Mathematics
- 7 December 2021

We work out the exact relationship between algebraic modular forms for a two-by-two general unitary group over a definite quaternion algebra, and those arising from genera of positive-definite… Expand

...

1

2

3

4

5

...