Works

Papers (Refereed)
  1. “Query obfuscation by semantic decomposition”, D. Bollegal, T. Machide and K. Kawarabayash, Proc. of the 13th Language Resources and Evaluation Conference (LREC 2022), pages 6200-6211.
  2. “A generating function to generalize the sum formula for quadruple zeta values”, T. Machide, Tokyo J. Math. 42 (2019) 329 - 355.
  3. “Identity involving symmetric sums of regularized multiple zeta-star values”, T. Machide, Mosc. J. Comb. Number Theory 8 (2019), 125-136.
  4. “Identities involving cyclic and symmetric sums of regularized multiple zeta values”, T. Machide, Pacific J. Math. 286 (2017), 307-359.
  5. “Congruence identities of regularized multiple zeta values involving a pair of index sets”, T. Machide,  Int. J. Number Theory 12 (2016), 409-426. 
  6. “Extended double shuffle relations and the generating function of triple zeta values of any fixed weight”, T. Machide, Kyushu J. Math. 26 (2013), 281-307. 
  7. “Generators for vector spaces spanned by double zeta values with even weight”, T. Machide, J. Number Theory 133 (2013), 2240-2246.
  8. “Some restricted sum formulas for double zeta values”, T. Machide, Proc. Japan Acad., Ser. A, 89 (2013), 51-54.
  9. “Weighted sums with two parameters of multiple zeta values and their formulas”, T. Machide, Int. J. Number Theory 8 (2012), 1903-1921.
  10. “An elliptic analogue of generalized Dedekind-Rademacher sums”, T. Machide, J. Number Theory 128 (2008), 1060-1073.
  11. “Sums of products of Kronecker’s double series”, T. Machide, J. Number Theory 128 (2008), 820-834.

Talks
  1. “Computational results on ranks of matrices of extended double shuffle relations for modulo 2”, Tomoya Machide, Tomohiro Sonobe, Japan-Taiwan joint workshop on multiple zeta values 2020, Feb. 2020, Okinawa-ken Seinen Kaikan (pdf)
  2. “On elliptic analogues of generalized Dedekind-Rademacher sums by use of Kronecker’s double series”, Tomoya Machide, Pure and Applied Number Theory School (L-functions, Dedekind Sums, Diophantine equations, permutation polynomials, modular forms), 2015, KAIST, Korea.
  3. “Quadruple zeta values and asymptotic properties of quadruple polylogarithms”, T. Machide, The 17th. Joint Workshop on Number Theory between Japan and Taiwan, Waseda University.
  4. “Triple zeta values and asymptotic properties of triple polylogarithms”, T. Machide, Analytic Number Theory -- Number Theory through Approximation and Asymptotics, Kyoto University.
  5. “A sum formula with three parameters for triple zeta values”, T. Machide, 2012 NCTS Japan-Taiwan Joint Conference on Number Theory, 2012年8月, National Tsing Hua University.
  6. “Elliptic Dedekind-Rademacher Sums and Transformation Formulae of Certain Infinite Series”, T. Machide, Automorphic Representations, Automorphic Form, L-functions, and Related Topics, Kyoto University.
  7. “Elliptic Dedekind-Rademacher Sums and Transformation Formulae of Certain Infinite Series”, T. Machide, Analytic Number Theory and Related Areas, Kyoto University.

Preprints
  1. “Computations about formal multiple zeta spaces defined by binary extended double shuffle relations”, T. Machide, preprint (2022), arXiv:2205.13751 [math.NT]. 
  2. “A formula for systems of Boolean polynomial equations and applications to computational complexity”, T. Machide, preprint (2019), arXiv:1907.09686 [math.LO]. 
  3. “An Elliptic Analogue Of Generalized Cotangent Dirichlet Series And Its Transformation Formulae At Some Integer Arguments”, T. Machide, preprint (2011), arXiv:1107.4933 [math.NT]. 
  4. “Elliptic Dedekind-Rademacher Sums and Transformation Formulae of Certain Infinite Series”, T. Machide, preprint (2007), Hokkaido Univ. Preprint Series # 863. 
  5. “Functional Equations and the Harmonic Relations for Multiple Zeta Values”, T. Machide, preprint (2006), Hokkaido Univ. Preprint Series # 765. 
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