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4 results on '"LAMPLUGH, JACK"'

1. An Euler system for characters over an imaginary biquadratic field

Author

Lamplugh, Jack

Subjects
Mathematics - Number Theory, 11F80, 11R23
Abstract

Given a pair of modular forms with complex multiplication by distinct imaginary quadratic fields, the four dimensional Galois representation associated to their Rankin--Selberg convolution is induced from a character over an imaginary biquadratic field $F$. Using the Euler system of Lei, Loeffler and Zerbes we bound a Selmer group associated to this character, over the unique $\mathbb{Z}_{p}^{3}$-extension of $F$., Comment: 21 pages

Published
2016

4. Triviality of the ℓ-class groups in $\mathbb{Z}_{p}$-extensions of $\mathbb{Q}(\sqrt{-1})$ for split primes p ≡ 1 modulo 4.

Author

LAMPLUGH, JACK

Subjects
*QUADRATIC fields, *ALGEBRAIC number theory, *ELLIPTIC functions, *APPLIED mathematics, *MATHEMATICAL analysis, *ALGEBRA, *ALGORITHMS
Abstract

In this paper we study the class numbers in the finite layers of certain non-cyclotomic $\mathbb{Z}$p-extensions of the imaginary quadratic field $\mathbb{Q}(\sqrt{-1})$, for all primes p ≡ 1 modulo 4. By studying the Mahler measure of elliptic units, we are able to show that there are only finitely many primes ℓ congruent to a primitive root modulo p2 that divide any of the class numbers in the $\mathbb{Z}$p-extension. [ABSTRACT FROM AUTHOR]

Published
2014
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