2 citations · 4 across the 11 of their papers we have counts for
13 papers
A framework for proving quantum modularity: Application to Witten's asymptotic expansion conjecture
Yuya Murakami
We address two linked problems at the interface of quantum topology and number theory: deriving asymptotic expansions of the Witten--Reshetikhin--Turaev invariants for 3-manifolds…
-function invariants for 3-manifolds and relations between generalized Bernoulli polynomials
Yuya Murakami
We introduce -functions attached to negative definite plumbed manifolds as the Mellin transforms of homological blocks. We prove that they are entire functions and their value…
A proof of The Radial Limit Conjecture for Costantino--Geer--Patureau-Mirand Quantum invariants
William Elbæk Mistegård, Yuya Murakami
For a negative definite plumbed three-manifold, we give an integral representation of the appropriate average of the GPPV invariants of Gukov--Pei--Putrov--Vafa, which implies that…
An asymptotic property on a reciprocity law for the Bettin--Conrey cotangent sum
Hirotaka Akatsuka, Yuya Murakami
In 2013 Bettin and Conrey have introduced a cotangent sum , which can be regarded as a variant of the Dedekind sum. They have discovered tha…
Homological blocks with simple Lie algebras and Witten--Reshetikhin--Turaev invariants
Yuya Murakami, Yuji Terashima
In this article, for any Seifert fibered homology 3-sphere, we introduce homological blocks with simple Lie algebra and prove that its radial limits are identified with the Witten-…
A proof of a conjecture of Gukov-Pei-Putrov-Vafa
Yuya Murakami
In this paper, we prove Gukov-Pei-Putrov-Vafa's conjecture that the Witten-Reshetikhin-Turaev invariants are radial limits of homological blocks, which are -series introduced…
Witten-Reshetikhin-Turaev invariants and indefinite false theta functions for plumbing indefinite H-graphs
Yuya Murakami
Gukov--Pei--Putrov--Vafa conjectured the existence of -series whose radial limits are Witten--Reshetikhin--Turaev invariants and called them homological blocks. For weakly neg…
Witten-Reshetikhin-Turaev invariants and homological blocks for plumbed homology spheres
Yuya Murakami
In this paper, we prove a conjecture by Gukov-Pei-Putrov-Vafa for a wide class of plumbed 3-manifolds. Their conjecture states that Witten-Reshetikhin-Turaev (WRT) invariants are r…
Witten-Reshetikhin-Turaev Invariants, Homological Blocks, and Quantum Modular Forms for Unimodular Plumbing H-Graphs
Akihito Mori, Yuya Murakami
Gukov-Pei-Putrov-Vafa constructed -series invariants called homological blocks in a physical way in order to categorify Witten-Reshetikhin-Turaev (WRT) invariants and conjecture…
Extended-cycle integrals of modular functions for badly approximable numbers
Yuya Murakami
Cycle integrals of modular functions are expected to play a role in real quadratic analogue of singular moduli. In this paper, we extend the definition of cycle integrals of modula…
Hurwitz class numbers with level and modular correspondences
Yuya Murakami
In this paper, we prove Hurwitz-Eichler type formulas for Hurwitz class numbers with each level when the modular curve has genus zero. A key idea is to calculate i…
A continuity of cycle integrals of modular functions
Yuya Murakami
In this paper we study a continuity of the "values" of modular functions at the real quadratic numbers which are defined in terms of their cycle integrals along the associated clos…
Intersection numbers of modular correspondences for genus zero modular curves
Yuya Murakami
In this paper, we introduce modular polynomials for the congruence subgroup when has genus zero and therefore the polynomials are defined by a Hauptmodul of $ X…