Ryotaro Sakamoto

activity

20162026

most citedOn the theory of higher rank Euler, Kolyvagin and Stark systems, II

21 citations · 72 across the 19 of their papers we have counts for

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17 papers · 1 filter

math.NT2026

Two Extremal Even Unimodular Lattices of Rank $88$

Ryotaro Sakamoto

In this paper, we construct two extremal positive definite even unimodular lattices of rank $88$ using a Hermitian tensor product over $Q (- 23)$ , thereby extending t…

math.NT2025

Wall-crossing and $p$ -adic Artin formalism for $GSp_{4} \times GL_{2} \times GL_{2}$

Kâzım Büyükboduk, Óscar Rivero, Ryotaro Sakamoto

The goal of this article is to develop a $p$ -adic Artin formalism in the context of $p$ -adic families of automorphic forms on $GSp_{4} \times GL_{2} \times GL_{2}$ . Our…

math.NT2025

Classifications of Hecke Fields and Galois Images of Weight One Exotic Newforms

Ryotaro Sakamoto, Sho Yoshikawa

We determine the Hecke fields associated with weight one newforms of $A_{4}$ -, $S_{4}$ -, and $A_{5}$ -type, expressed in terms of the order of its nebentypus. Furthermore, for each type,…

math.NT2025

On the Artin formalism for triple product $p$ -adic $L$ -functions

Kâzım Büyükboduk, Ryotaro Sakamoto

Our main objective in the present article is to study the factorisation problem for triple-product $p$ -adic $L$ -functions, particularly in the scenarios when the defining propertie…

math.NT2023

On the Artin formalism for triple product $p$ -adic $L$ -functions: Super-factorization

Kâzım Büyükboduk, Daniele Casazza

We prove the factorization conjecture for triple-product $p$ -adic $L$ -functions formulated in a companion article in the special case when two of the (three) factors have complex m…

math.NT2021★ 1 cited

$p$ -Selmer group and Modular symbols

Ryotaro Sakamoto

In this paper, we prove that the dimension of the $p$ -Selmer group for an elliptic curve is controlled by certain analytic quantities associated with modular symbols, which is conj…

math.NT2020★ 7 cited

Euler Systems for $GSp_{4} \times GL_{2}$

Chi-Yun Hsu, Zhaorong Jin, Ryotaro Sakamoto

For a non-endoscopic cohomological cuspidal automorphic representation of $GSp_{4} \times GL_{2}$ , assumed to be $p$ -ordinary, we construct an Euler system for the Ga…

math.NT2020

$L$ -invariants, $p$ -adic heights and factorization of $p$ -adic $L$ -functions

Kâzim Büyükboduk, Ryotaro Sakamoto

We continue with our study of the non-critical exceptional zeros of Katz' $p$ -adic $L$ -functions attached to a CM field $K$ , following two threads. In the first thread, we redefine…

math.NT2020

Notes on the module of Euler systems

Ryotaro Sakamoto

In this paper, we study the module of Euler systems. We determine the ideal of an Iwasawa algebra associated with Euler systems of rank $0$ . We also show that the module of higher…

math.NT2020★ 9 cited

A higher rank Euler system for the multiplicative group over a totally real field

Ryotaro Sakamoto

In this paper, we construct a higher rank Euler system for the multiplicative group over a totally real field by using the Iwasawa main conjecture proved by Wiles. A key ingredient…

math.NT2019★ 3 cited

On the non-critical exceptional zeros of Katz $p$ -adic $L$ -functions for CM fields

Kazim Buyukboduk, Ryotaro Sakamoto

The primary goal of this article is to study $p$ -adic Beilinson conjectures in the presence of exceptional zeros for Artin motives over CM fields. In more precise terms, we address…

math.NT2019★ 3 cited

On the theory of higher rank Euler, Kolyvagin and Stark systems, IV: the multiplicative group

David Burns, Ryotaro Sakamoto, Takamichi Sano

We describe a refinement of the general theory of higher rank Euler, Kolyvagin and Stark systems in the setting of the multiplicative group over arbitrary number fields. We use the…

math.NT2019

Iwahori-Hecke algebra and unramified local L-functions

Masao Oi, Ryotaro Sakamoto, Hiroyoshi Tamori

In this paper, we compute the Hecke action of a certain test function on the space of an unramified principal series of a connected reductive group over a non-archimedean local fie…

math.NT2019★ 11 cited

On the theory of higher rank Euler, Kolyvagin and Stark systems, III: applications

David Burns, Ryotaro Sakamoto, Takamichi Sano

In an earlier article we proved the existence of a canonical Kolyvagin derivative homomorphism between the modules of Euler and Kolyvagin systems (in any given rank) that are assoc…

math.NT2018★ 21 cited

On the theory of higher rank Euler, Kolyvagin and Stark systems, II

David Burns, Ryotaro Sakamoto, Takamichi Sano

We prove the existence of a canonical `higher Kolyvagin derivative' homomorphism between the modules of higher rank Euler systems and higher rank Kolyvagin systems, as has been con…

math.NT2016★ 1 cited

On the theory of higher rank Euler, Kolyvagin and Stark systems

David Burns, Takamichi Sano

Mazur and Rubin have recently developed a theory of higher rank Kolyvagin and Stark systems over principal artinian rings and discrete valuation rings. In this article we describe…

math.NT2016★ 4 cited

Stark Systems over Gorenstein Local Rings

Ryotaro Sakamoto

In this paper, we define a module of Stark systems over a complete Gorenstein local ring with a finite residue field of odd characteristic. Under some mild assumptions, we show tha…

Two Extremal Even Unimodular Lattices of Rank 88

Wall-crossing and p-adic Artin formalism for GSp4​×GL2​×GL2​

Classifications of Hecke Fields and Galois Images of Weight One Exotic Newforms

On the Artin formalism for triple product p-adic L-functions

On the Artin formalism for triple product p-adic L-functions: Super-factorization

p-Selmer group and Modular symbols

Euler Systems for GSp4​×GL2​

L-invariants, p-adic heights and factorization of p-adic L-functions

Notes on the module of Euler systems

A higher rank Euler system for the multiplicative group over a totally real field

On the non-critical exceptional zeros of Katz p-adic L-functions for CM fields

On the theory of higher rank Euler, Kolyvagin and Stark systems, IV: the multiplicative group

Iwahori-Hecke algebra and unramified local L-functions

On the theory of higher rank Euler, Kolyvagin and Stark systems, III: applications

On the theory of higher rank Euler, Kolyvagin and Stark systems, II

On the theory of higher rank Euler, Kolyvagin and Stark systems

Stark Systems over Gorenstein Local Rings

Two Extremal Even Unimodular Lattices of Rank $88$

Wall-crossing and $p$ -adic Artin formalism for $GSp_{4} \times GL_{2} \times GL_{2}$

On the Artin formalism for triple product $p$ -adic $L$ -functions

On the Artin formalism for triple product $p$ -adic $L$ -functions: Super-factorization

$p$ -Selmer group and Modular symbols

Euler Systems for $GSp_{4} \times GL_{2}$

$L$ -invariants, $p$ -adic heights and factorization of $p$ -adic $L$ -functions

On the non-critical exceptional zeros of Katz $p$ -adic $L$ -functions for CM fields