28 citations · 61 across the 25 of their papers we have counts for
26 papers
Symmetric multiple Eisenstein series
Takashi Hara, Kenji Sakugawa, Koji Tasaka
In this paper, we introduce the symmetric multiple Eisenstein series, a variant of the multiple Eisenstein series. As a fundamental result, we show that they satisfy the linear shu…
Spherical designs for finite quaternionic unit groups and their applications to modular forms
Masatake Hirao, Hiroshi Nozaki, Koji Tasaka
For a finite subset of the -dimensional unit sphere, the harmonic strength of is the set of such that for all harmonic…
Catalogue of modular relations for double zeta values
Koji Tasaka
This note is a compilation of related research on modular relations for multiple zeta values. Roughly speaking, modular relations are (homogeneous) linear relations of multiple zet…
The harmonic strength of shells of lattices and weighted theta series
Koji Tasaka
This is the write-up of a talk given in RIMS conference ``Analytic and arithmetic aspects of automorphic representations", where I outlined two kinds of different results related t…
Spherical designs and modular forms of the lattice
Masatake Hirao, Hiroshi Nozaki, Koji Tasaka
In this paper, we study shells of the lattice with a {slight generalization} of spherical -designs due to Delsarte-Goethals-Seidel, namely, the spherical design of harmoni…
The ring of finite algebraic numbers and its application to the law of decomposition of primes
Julian Rosen, Yoshihiro Takeyama, Koji Tasaka +1
In this paper, we develop an explicit method to express finite algebraic numbers (in particular, certain idempotents among them) in terms of linear recurrent sequences, and give ap…
On a unified double zeta function of Mordell--Tornheim type
Shin-ya Kadota, Takuya Okamoto, Masataka Ono +1
We introduce the unified double zeta function of Mordell--Tornheim type and compute its values at non-positive integer points. We then discuss a possible generalization of the Kane…
Supercongruences of multiple harmonic -sums and generalized finite/symmetric multiple zeta values
Yoshihiro Takeyama, Koji Tasaka
The Kaneko--Zagier conjecture describes a correspondence between finite multiple zeta values and symmetric multiple zeta values. Its refined version has been established by Jarossa…
Finite and symmetric Mordell-Tornheim multiple zeta values
Henrik Bachmann, Yoshihiro Takeyama, Koji Tasaka
We introduce finite and symmetric Mordell-Tornheim type of multiple zeta values and give a new approach to the Kaneko-Zagier conjecture stating that the finite and symmetric multip…
Finite and symmetric colored multiple zeta values and multiple harmonic q-series at roots of unity
Koji Tasaka
The Kaneko-Zagier conjecture states that finite and symmetric multiple zeta values satisfy the same relations. In the previous work with H.~Bachmann and Y.~Takeyama, we proved that…
Hecke eigenform and double Eisenstein series
Koji Tasaka
Cusp forms for the full modular group can be written as linear combination of double Eisenstein series introduced by Gangl, Kaneko and Zagier. We give an explicit formula for decom…
Special values of finite multiple harmonic q-series at roots of unity
Henrik Bachmann, Yoshihiro Takeyama, Koji Tasaka
We study special values of finite multiple harmonic q-series at roots of unity. These objects were recently introduced by the authors and it was shown that they have connections to…
On Ecalle's and Brown's polar solutions to the double shuffle equations modulo products
Nils Matthes, Koji Tasaka
Two explicit sets of solutions to the double shuffle equations modulo products were introduced by Ecalle and Brown respectively. We place the two solutions into the same algebraic…
Relationships between multiple zeta values of depths 2 and 3 and period polynomials
Ding Ma, Koji Tasaka
Some combinatorial aspects of relations between multiple zeta values of depths 2 and 3 and period polynomials are discussed.
Cyclotomic analogues of finite multiple zeta values
Henrik Bachmann, Yoshihiro Takeyama, Koji Tasaka
We introduce the notion of finite multiple harmonic q-series at a primitive root of unity and show that these specialize to the finite multiple zeta value (FMZV) and the symmetrize…
Duality/Sum formulas for iterated integrals and their application to multiple zeta values
Minoru Hirose, Kohei Iwaki, Nobuo Sato +1
We investigate linear relations among a class of iterated integrals on the Riemann sphere minus four points and . Generalization of the duality formula and the sum…
Evaluation of Tornheim's type of double series
Shin-ya Kadota, Takuya Okamoto, Koji Tasaka
We examine values of certain Tornheim's type of double series with odd weight. As a result, an affirmative answer to a conjecture about the parity theorem for the zeta function of…
On triple zeta values of even weight and their connections with period polynomials
Ding Ma, Koji Tasaka
We study triple zeta values of even weight and show various connections with period polynomials. As a result, an (expected) upper bound of the dimension of the vector space spanned…
The double shuffle relations for multiple Eisenstein series
Henrik Bachmann, Koji Tasaka
We study the multiple Eisenstein series introduced by Gangl, Kaneko and Zagier. We give a proof of (restricted) finite double shuffle relations for multiple Eisenstein series by de…
Eisenstein series identities based on partial fraction decomposition
Minoru Hirose, Nobuo Sato, Koji Tasaka
From the theory of modular forms, there are exactly linear relations among the Eisenstein series and its products . We present…
On linear relations among totally odd multiple zeta values related to period polynomials
Koji Tasaka
We show that there is a relationship between modular forms and totally odd multiple zeta values, by relating the matrix , whose entries are given by the polynomial represe…
Modular parametrizations of certain elliptic curves
Matija Kazalicki, Yuichi Sakai, Koji Tasaka
Kaneko and Sakai recently observed that certain elliptic curves whose associated newforms (by the modularity theorem) are given by the eta-quotients can be characterized by a parti…
On some multiple zeta-star values of one-two-three indices
Koji Tasaka, Shuji Yamamoto
In this paper, we present some identities for multiple zeta-star values with indices obtained by inserting 3 or 1 into the string 2,...,2. Our identities give analogues of Zagier's…
On a conjecture for representations of integers as sums of squares and double shuffle relations
Koji Tasaka
In this paper, we prove a conjecture of Chan and Chua for the number of representations of integers as sums of 8s integral squares. The proof uses a theorem of Imamoglu and Kohnen,…