ISSN 0030-1566

M ATHEMATICAL J OURNALOFO KAYAMA U NIVERSITY
VOL. 65 2023

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DEPARTMENT OF MATHEMATICSFACULTY OF SCIENCEOKAYAMA UNIVERSITYOKAYAMA, JAPANMJOURNAL
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CONTENTSPage
Hoshi, Y.

A Note on Fields Generated by Jacobi Sums . . . . . . . . . . . 117

Kametaka, Y., Watanabe, K., Nagai, N.,
Takemura, K. and Yamagishi, H. Positivity andHierarchical Structure of four Green Functions
Corresponding to a Bending Problem of a Beam on a halfline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Kato, R. E(2)-local Picard graded beta elements at theprime three . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

Kinjo, T. Non-Modular Solution of the Kaneko-Zagier
Equations with respect to Fricke Groups of Low Levels . . . . . . . . . . . .

83

A characterization of the class of Harada rings . . . . . . . . .

1

Kusuoka, Sei. An improvement of the integrability of thestate space of the Φ43 -process and the support of theΦ43 -measure constructed by the limit of stationary processesof approximating stochastic quantization equations . . . . . . . . . . . . . . . .

97

Morita, J., Pianzola, A. and Shibata, T. Aﬃne
Kac-Moody Groups as Twisted Loop Groups obtained by
Galois Descent Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

Koike, K.

Wah Wah and Taniguchi, M. Traveling front solutions
for perturbed reaction-diﬀusion equations . . . . . . . . . . . . . . . . . . . . . . . . . 125

JANUARY 2023
Vol. 65

CONTENTS
Page
Koike, K.

A characterization of the class of Harada rings . . . . . . . . . . . . . . . . . . .

1

Kato, R.

E(2)-local Picard graded beta elements at the prime three . . . . . . . . . .

23

Morita, J., Pianzola, A. and Shibata, T. Aﬃne Kac-MoodyGroups as Twisted Loop Groups obtained by Galois DescentConsiderations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

Kinjo, T. Non-Modular Solution of the Kaneko-Zagier Equations withrespect to Fricke Groups of Low Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

Kusuoka, Sei. An improvement of the integrability of the state spaceof the Φ43 -process and the support of the Φ43 -measure constructed by
the limit of stationary processes of approximating stochastic
quantization equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

Hoshi, Y.

A Note on Fields Generated by Jacobi Sums . . . . . . . . . . . . . . . . . . . . . 117

Wah Wah and Taniguchi, M. Traveling front solutions for perturbed
reaction-diﬀusion equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Kametaka, Y., Watanabe, K., Nagai, N., Takemura, K. andYamagishi, H. Positivity and Hierarchical Structure of four Green
Functions Corresponding to a Bending Problem of a Beam on a halfline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

A CHARACTERIZATION OF THE CLASS OF HARADA
RINGS
Kazutoshi KOIKE

Reprinted from Mathematical Journal of Okayama University
Vol. 65, 2023

E(2)-LOCAL PICARD GRADED BETA ELEMENTS AT THE
PRIME THREE
Ryo KATO

Reprinted from Mathematical Journal of Okayama University
Vol. 65, 2023

AFFINE KAC-MOODY GROUPS AS TWISTED LOOPGROUPS OBTAINED BY GALOIS DESCENTCONSIDERATIONS
Dedicated to Professor Robert V. Moody on the occasion of his 80th birthday.

Jun MORITA, Arturo PIANZOLA and Taiki SHIBATA

Reprinted from Mathematical Journal of Okayama University
Vol. 65, 2023

NON-MODULAR SOLUTION OF THE KANEKO-ZAGIEREQUATIONS WITH RESPECT TO FRICKE GROUPS OFLOW LEVELS
Toshiteru KINJO

Reprinted from Mathematical Journal of Okayama UniversityVol. 65, 2023

AN IMPROVEMENT OF THE INTEGRABILITY OF THE
STATE SPACE OF THE Φ43 -PROCESS AND THE SUPPORTOF THE Φ43 -MEASURE CONSTRUCTED BY THE LIMITOF STATIONARY PROCESSES OF APPROXIMATING
STOCHASTIC QUANTIZATION EQUATIONS
Seiichiro KUSUOKA

Reprinted from Mathematical Journal of Okayama University
Vol. 65, 2023

A NOTE ON FIELDS GENERATED BY JACOBI SUMS
Yuichiro HOSHI

Reprinted from Mathematical Journal of Okayama University
Vol. 65, 2023

TRAVELING FRONT SOLUTIONS FOR PERTURBEDREACTION-DIFFUSION EQUATIONSWah Wah and Masaharu TANIGUCHI

Reprinted from Mathematical Journal of Okayama University
Vol. 65, 2023

POSITIVITY AND HIERARCHICAL STRUCTURE OF
FOUR GREEN FUNCTIONS CORRESPONDING TO A
BENDING PROBLEM OF A BEAM ON A HALF LINEYoshinori KAMETAKA, Kohtaro WATANABE, Atsushi NAGAI, Kazuo
TAKEMURA and Hiroyuki YAMAGISHI

Reprinted from Mathematical Journal of Okayama University
Vol. 65, 2023