Antonio Lei

activity

20092026

most citedEuler systems for Rankin--Selberg convolutions of modular forms

88 citations · 416 across the 62 of their papers we have counts for

collaborators

64 papers

math.NT2026

Iwasawa theory of CM elliptic curves at potentially supersingular primes

Ben Forrás, Antonio Lei

We develop a plus and minus Iwasawa theory for CM elliptic curves with potentially supersingular reduction at a prime $p \geq 5$ . We construct local points that satisfy suitable "jump…

math.CO2026

Recovering Laplacian Lattices from $L$ -Functions of Graphs

Daniel Labib, Antonio Lei

We introduce $L$ -functions associated with characters of the Jacobian of a finite graph, as a graph-theoretic analogue of the $L$ -functions arising from unramified coverings of alg…

math.NT2023★ 4 cited

Algebraic structure and characteristic ideals of fine Mordell--Weil groups and plus/minus Mordell--Weil groups

Antonio Lei

Given an elliptic curve defined over a number field $F$ , we study the algebraic structure and prove a control theorem for Wuthrich's fine Mordell--Weil groups over a $Z_{p}$ …

math.NT2023★ 2 cited

A remark on the characteristic elements of anticyclotomic Selmer groups of elliptic curves with complex multiplication at supersingular primes

Antonio Lei

Let $p \geq 5$ be a prime number. Let $E / Q$ be an elliptic curve with complex multiplication by an imaginary quadratic field $K$ such that $p$ is inert in $K$ and that $E$ ha…

math.NT2023

On the Zeta functions of supersingular isogeny graphs and modular curves

Antonio Lei, Katharina Müller

Let $p$ and $q$ be distinct prime numbers, with $q \equiv 1 (mod 12)$ . Let $N$ be a positive integer that is coprime to $pq$ . We prove a formula relating the Hasse--Weil zeta functi…

math.NT2023

On ordinary isogeny graphs with level structure

Antonio Lei, Katharina Müller

Let $l$ and $p$ be two distinct prime numbers. We study $l$ -isogeny graphs of ordinary elliptic curves defined over a finite field of characteristic $p$ , together with a level stru…

math.NT2023

Growth of $p$ -parts of ideal class groups and fine Selmer groups in $Z_{q}$ -extensions with $p \neq = q$

Debanjana Kundu, Antonio Lei

Fix two distinct odd primes $p$ and $q$ . We study " $p \neq = q$ " Iwasawa theory in two different settings. Let $K$ be an imaginary quadratic field of class number 1 such that both $p$ …

math.NT2023

On the Iwasawa invariants of BDP Selmer groups and BDP P-adic L-fucntions

Antonio Lei, Katharina Müller, Jiacheng Xia

Let $p$ be an odd prime. Let $f_{1}$ and $f_{2}$ be weight-two Hecke eigen-cuspforms with isomorphic residual Galois representations at $p$ . Greenberg--Vatsal and Emerton--Pollack--Wes…

math.NT2022

On the BDP Iwasawa main conjecture for modular forms

Antonio Lei, Luochen Zhao

Let $K$ be an imaginary quadratic field where $p$ splits, $p \geq 5$ a prime number and $f$ an eigen-newform of even weight and level $N > 3$ that is coprime to $p$ . Under the Heegner…

math.NT2022

Anticyclotomic Iwasawa theory of abelian varieties of $GL_{2}$ -type at non-ordinary primes

Ashay Burungale, Kâzım Büyükboduk, Antonio Lei

Let $p \geq 5$ be a prime number, $E / Q$ an elliptic curve with good supersingular reduction at $p$ and $K$ an imaginary quadratic field such that the root number of $E$ over…

math.NT2022

Lambda-invariants of Mazur--Tate elements attached to Ramanujan's tau function and congruences with Eisenstein series

Anthony Doyon, Antonio Lei

Let $p \in {3, 5, 7}$ and let $Δ$ denote the weight twelve modular form arising from Ramanujan's tau function. We show that $Δ$ is congruent to an Eisenstein series $E_{k, χ, ψ}$ modu…

math.NT2022★ 1 cited

Studying Hilbert's 10th problem via explicit elliptic curves

Debanjana Kundu, Antonio Lei, Florian Sprung

N.García-Fritz and H.Pasten showed that Hilbert's 10th problem is unsolvable in the ring of integers of number fields of the form $Q (3 p, - q)$ for positive p…

math.CO2022★ 6 cited

On the distribution of Iwasawa invariants associated to multigraphs

Cédric Dion, Antonio Lei, Anwesh Ray +1

Let $ℓ$ be a prime number. The Iwasawa theory of multigraphs is the systematic study of growth patterns in the number of spanning trees in abelian $ℓ$ -towers of multigraphs.…

math.NT2022

Asymptotic formula for Tate-Shafarevich groups of $p$ -supersingular elliptic curves over anticyclotomic extensions

Antonio Lei, Meng Fai Lim, Katharina Müller

Let $p \geq 5$ be a prime number and $E / Q$ an elliptic curve with good supersingular reduction at $p$ . Under the generalized Heegner hypothesis, we investigate the $p$ -prima…

math.NT2022

Control theorems for fine Selmer groups, and duality of fine Selmer groups attached to modular forms

Jeffrey Hatley, Debanjana Kundu, Antonio Lei +1

Let $O$ be the ring of integers of a finite extension of $Q_{p}$ . We prove two control theorems for fine Selmer groups of general cofinitely generated modules over…

math.CO2022

The non- $ℓ$ -part of the number of spanning trees in abelian $ℓ$ -towers of multigraphs

Antonio Lei, Daniel Vallières

Let $ℓ$ and $p$ be two distinct primes. We study the $p$ -adic valuation of the number of spanning trees in an abelian $ℓ$ -tower of connected multigraphs. This is analogous to…

math.NT2021

Arithmetic Statistics and noncommutative Iwasawa Theory

Debanjana Kundu, Antonio Lei, Anwesh Ray

Let $p$ be an odd prime. Associated to a pair $(E, F_{\infty})$ consisting of a rational elliptic curve $E$ and a $p$ -adic Lie extension $F_{\infty}$ of $\mathbb{Q}…

math.NT2021★ 4 cited

On fine Selmer groups and signed Selmer groups of elliptic modular forms

Antonio Lei, Meng Fai Lim

Let $f$ be an elliptic modular form and $p$ an odd prime that is coprime to the level of $f$ . We study the link between divisors of the characteristic ideal of the $p$ -primary fine…

math.NT2021★ 3 cited

On Certain Probabilistic Properties of Polynomials over the Ring of $p$ -adic Integers

Antonio Lei, Antoine Poulin

In this article, we study several probabilistic properties of polynomials defined over the ring of $p$ -adic integers under the Haar measure. First, we calculate the probability tha…

math.NT2021★ 2 cited

Congruences between Ramanujan's tau function and elliptic curves, and Mazur--Tate elements at additive primes

Anthony Doyon, Antonio Lei

We show that if $E / Q$ is an elliptic curve with a rational $p$ -torsion for $p = 2$ or $3$ , then there is a congruence relation between Ramanujan's tau function and $E$ modul…

math.NT2021★ 4 cited

On fine Selmer groups and the greatest common divisor of signed and chromatic $p$ -adic $L$ -functions

Antonio Lei, R. Sujatha

Let $E / Q$ be an elliptic curve and $p$ an odd prime where $E$ has good supersingular reduction. Let $F_{1}$ denote the characteristic power series of the Pontryagin dual of…

math.NT2021★ 4 cited

On Selmer groups in the supersingular reduction case

Antonio Lei, R. Sujatha

Let $p$ be a fixed odd prime. Let $E$ be an elliptic curve defined over a number field $F$ with good supersingular reduction at all primes above $p$ . We study both the classical an…

math.NT2020

Iwasawa theory of automorphic representations of $GL_{2 n}$ at non-ordinary primes

Antonio Lei, Jishnu Ray

Let $Π$ be a cuspidal automorphic representation of $GL_{2 n} (A_{Q})$ and let $p$ be an odd prime at which $Π$ is unramified. In a recent work, Barrera, Dimitrov and…

math.NT2020★ 10 cited

Comparing anticyclotomic Selmer groups of positive coranks for congruent modular forms -- Part II

Jeffrey Hatley, Antonio Lei

We study the Selmer group associated to a $p$ -ordinary newform $f \in S_{2 r} (Γ_{0} (N))$ over the anticyclotomic $Z_{p}$ -extension of an imaginary quadratic field $K/\mathbb{Q}…

Iwasawa theory of CM elliptic curves at potentially supersingular primes

Recovering Laplacian Lattices from L-Functions of Graphs

Algebraic structure and characteristic ideals of fine Mordell--Weil groups and plus/minus Mordell--Weil groups

A remark on the characteristic elements of anticyclotomic Selmer groups of elliptic curves with complex multiplication at supersingular primes

On the Zeta functions of supersingular isogeny graphs and modular curves

On ordinary isogeny graphs with level structure

Growth of p-parts of ideal class groups and fine Selmer groups in Zq​-extensions with p=q

On the Iwasawa invariants of BDP Selmer groups and BDP P-adic L-fucntions

On the BDP Iwasawa main conjecture for modular forms

Anticyclotomic Iwasawa theory of abelian varieties of GL2​-type at non-ordinary primes

Lambda-invariants of Mazur--Tate elements attached to Ramanujan's tau function and congruences with Eisenstein series

Studying Hilbert's 10th problem via explicit elliptic curves

On the distribution of Iwasawa invariants associated to multigraphs

Asymptotic formula for Tate-Shafarevich groups of p-supersingular elliptic curves over anticyclotomic extensions

Control theorems for fine Selmer groups, and duality of fine Selmer groups attached to modular forms

The non-ℓ-part of the number of spanning trees in abelian ℓ-towers of multigraphs

Arithmetic Statistics and noncommutative Iwasawa Theory

On fine Selmer groups and signed Selmer groups of elliptic modular forms

On Certain Probabilistic Properties of Polynomials over the Ring of p-adic Integers

Congruences between Ramanujan's tau function and elliptic curves, and Mazur--Tate elements at additive primes

On fine Selmer groups and the greatest common divisor of signed and chromatic p-adic L-functions

On Selmer groups in the supersingular reduction case

Iwasawa theory of automorphic representations of GL2n​ at non-ordinary primes

Comparing anticyclotomic Selmer groups of positive coranks for congruent modular forms -- Part II

Recovering Laplacian Lattices from $L$ -Functions of Graphs

Growth of $p$ -parts of ideal class groups and fine Selmer groups in $Z_{q}$ -extensions with $p \neq = q$

Anticyclotomic Iwasawa theory of abelian varieties of $GL_{2}$ -type at non-ordinary primes

Asymptotic formula for Tate-Shafarevich groups of $p$ -supersingular elliptic curves over anticyclotomic extensions

The non- $ℓ$ -part of the number of spanning trees in abelian $ℓ$ -towers of multigraphs

On Certain Probabilistic Properties of Polynomials over the Ring of $p$ -adic Integers

On fine Selmer groups and the greatest common divisor of signed and chromatic $p$ -adic $L$ -functions

Iwasawa theory of automorphic representations of $GL_{2 n}$ at non-ordinary primes