Works


Papers (Refereed)
  1. “Identities involving cyclic and symmetric sums of regularized multiple zeta values”, T. Machide, to appear in Pacific Journal of Mathematics. (Note: the title is changed.)
  2. “Congruence identities of regularized multiple zeta values involving a pair of index sets”, T. Machide,  Int. J. Number Theory 12 (2016), 409-426. 
  3. “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. 
  4. “Generators for vector spaces spanned by double zeta values with even weight”, T. Machide, J. Number Theory 133 (2013), 2240-2246.
  5. “Some restricted sum formulas for double zeta values”, T. Machide, Proc. Japan Acad., Ser. A, 89 (2013), 51-54.
  6. “Weighted sums with two parameters of multiple zeta values and their formulas”, T. Machide, Int. J. Number Theory 8 (2012), 1903-1921.
  7. “An elliptic analogue of generalized Dedekind-Rademacher sums”, T. Machide, J. Number Theory 128 (2008), 1060-1073.
  8. “Sums of products of Kronecker’s double series”, T. Machide, J. Number Theory 128 (2008), 820-834.


Talks
  1. “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.
  2. “Quadruple zeta values and asymptotic properties of quadruple polylogarithms”, T. Machide, The 17th. Joint Workshop on Number Theory between Japan and Taiwan, Waseda University.
  3. “Triple zeta values and asymptotic properties of triple polylogarithms”, T. Machide, Analytic Number Theory -- Number Theory through Approximation and Asymptotics, Kyoto University.
  4. “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.
  5. “Elliptic Dedekind-Rademacher Sums and Transformation Formulae of Certain Infinite Series”, T. Machide, Automorphic Representations, Automorphic Form, L-functions, and Related Topics, Kyoto University.
  6. “Elliptic Dedekind-Rademacher Sums and Transformation Formulae of Certain Infinite Series”, T. Machide, Analytic Number Theory and Related Areas, Kyoto University.