Some restricted sum formulas for double zeta values

Machide, Tomoya

doi:10.3792/pjaa.89.51

Cited by 5 publications

(9 citation statements)

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“…Notice that we do not require our k to be odd in this case. It is worth pointing out that our result above is compatible with Theorem 1.1 in [7] by Machide, which gives some restricted sum formulas for double zeta values. For example, when k ≡ 0 mod 3, Machide proves that…”

Section: Introduction and Main Resultssupporting

confidence: 86%

“…For k = 12 and k = 16, the first two cases for which there are non-zero cusp forms on SL 2 (Z), we have the following identities. 5197 691 ζ(12) = 28ζ(9, 3) + 150ζ(7, 5) + 168ζ (5,7) 78967 3617 ζ(16) = 66ζ(13, 3) + 375ζ(11, 5) + 686ζ(9, 7) + 675ζ (7,9) + 396ζ (5,11).…”

Section: Ding Mamentioning

confidence: 99%

“…7 + 161x 6 + 21x 5 − 161x 4 − 144x 3 − 36x 2 , so the b r,s of the theorem are given (after multiplication by 330) by…”

mentioning

confidence: 99%

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Period polynomial relations between formal double zeta values of odd weight

2015

Math. Ann.

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Abstract. For odd k, we give a formula for the relations between double zeta values ζ(r, k − r) with r even. This formula provides a connection with the space of cusp forms on SL 2 (Z). This is the odd weight analogue of a result in [4] by Gangl, Kaneko and Zagier.We also provide an answer of a question asked by Zagier in [10] about the left kernel of some matrix. Although the restricted sum statement in [4] fails in the odd weight case, we provide an asymptotical statement that replaces it. Our statement works more generally for restricted sums with any congruence condition on the first entry of the double zeta value.

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Section: Introduction and Main Resultssupporting

confidence: 86%

Section: Ding Mamentioning

confidence: 99%

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Period polynomial relations between formal double zeta values of odd weight

2015

Math. Ann.

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“…Let N be the set of positive integers and m mean a lattice point (m 1 , m 2 , m 3 , m 4 ) in N 4 . Since A, C ∪ C (14) and C are transversals of certain quotient sets, the lattice points in N 4 decompose into the following disjoint subsets; We prepare some equations in order to prove Proposition 2.1, which are obtained by summing up each harmonic relation in Lemma 2.2 with (l…”

Section: An Identity Derived From Harmonic Relationsmentioning

confidence: 99%

“…Various generalizations of the sum formula have been studied: Ohno's relations, the cyclic, restricted and weighted sum formulas [1,5,8,10,14,15,16,17,18,19,20]. Recently parameterized generalizations of the sum formula, which we call parameterized sum formulas, were given for double and triple zeta values [3,13].…”

Section: Introductionmentioning

confidence: 99%