CiNii Articles - Fourier coefficients of modular forms

1

Differential operators on modular forms associated to Jacobi forms

Lee Min Ho

… Given Jacobi forms, we determine associated Jacobi-like forms, whose coeﬃcients are quasimodular forms. … We then use these quasimodular forms to construct diﬀerential operators on modular forms, which are expressed in terms of the Fourier coeﬃcients of the given Jacobi forms. …

Mathematical Journal of Okayama University 63(1), 123-131, 2021-01

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2

The Fourier coefficients of the McKay-Thompson series and the traces of CM values, an announcement (Algebraic Number Theory and Related Topics 2016)

Matsusaka Toshiki

… The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.This is an announcement of our results [8] on the arithmetic formulas for the Fouriercoefficients of the McKay-Thompson series of square-free level N.The elliptic modular function j(Ƭ) enjoys many beautiful properties. …

数理解析研究所講究録別冊 = RIMS Kokyuroku Bessatsu (B77), 259-263, 2020-04

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3

Flavor moonshine

Shotaro Shiba Funai , Hirotaka Sugawara

… precisely, their mass ratios) are expressed as coefficients in the Fourier expansion of some modular forms just as, in mathematics, dimensions of representations of a certain group are expressed as coefficients in the Fourier expansion of some modular forms. …

Progress of Theoretical and Experimental Physics 2020(1), 2020-01-13

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4

ON EXTREMAL QUASI-MODULAR FORMS AFTER KANEKO AND KOIKE

PELLARIN Federico , NEBE Gabriele

… Kaneko and Koike introduced the notion of extremal quasi-modular forms and proposed conjectures on their arithmetic properties. … The aim of this paper is to prove a rather sharp multiplicity estimate for these quasi-modular forms. …

Kyushu Journal of Mathematics 74(2), 401-413, 2020

J-STAGE
5

Explicit refinements of Böcherer's conjecture for Siegel modular forms of squarefree level

Dickson Martin , Pitale Ameya , Saha Abhishek , Schmidt Ralf

… We formulate an explicit refinement of Böcherer's conjecture for Siegel modular forms of degree 2 and squarefree level, relating weighted averages of Fourier coefficients with special values of 𝐿-functions. …

Journal of the Mathematical Society of Japan 72(1), 251-301, 2020

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6

Nonvanishing properties of Fourier coefficients for Siegel modular forms

Bocherer Siegfried , Das Soumya

数理解析研究所講究録 (2136), 127-133, 2019-12

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7

RANKIN-SELBERG METHOD FOR JACOBI FORMS OF INTEGRAL WEIGHT AND OF HALF-INTEGRAL WEIGHT ON SYMPLECTIC GROUPS

HAYASHIDA Shuichi

… In this article we show analytic properties of certain Rankin-Selberg type Dirichlet series for holomorphic Jacobi cusp forms of integral weight and of half-integral weight. … The numerators of these Dirichlet series are the inner products of Fourier-Jacobi coefficients of two Jacobi cusp forms. …

Kyushu Journal of Mathematics 73(2), 391-415, 2019

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8

Shifted products of Fourier coefficients of Siegel cusp forms of degree two

Kohnen Winfried , Sengupta Jyoti

… We prove a non-negativity result for shifted products of two Fourier coefficients of a Siegel Hecke eigenform of degree two not in the Maass space. …

Journal of the Mathematical Society of Japan 69(3), 1099-1103, 2017

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9

Introduction to the computational theory of elliptic modular forms (Algebraic Number Theory and Related Topics 2013) [in Japanese]

Yokoyama Shun'ichi

… The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. …

RIMS Kokyuroku Bessatsu (B53), 279-304, 2015-09

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10

Remark on Sturm bounds for Siegel modular forms of degree 2

KIKUTA Toshiyuki

Proceedings of the Japan Academy. Ser. A, Mathematical Sciences 91(6), 82-84, 2015-06
11

On the Siegel Eisenstein series of degree two for low weights

Gunji Keiichi

… In this paper, we give the Fourier coefficients of Siegel Eisenstein series of degree 2, level p, in order to calculate the dimensions of the space of Eisenstein series for low weights. … The main methods of the calculation is to compute the Siegel series of level p …

Journal of the Mathematical Society of Japan 67(3), 1043-1067, 2015

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12

CHARACTERIZING ADELIC HILBERT MODULAR CUSP FORMS BY COEFFICIENT SIZE

LINOWITZ Benjamin

… Associated with an adelic Hilbert modular form is a sequence of 'Fourier coefficients' which uniquely determine the form. … In this paper we characterize adelic Hilbert modular cusp forms by the size of their Fourier coefficients. …

Kyushu Journal of Mathematics 68(1), 105-111, 2014

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13

On the growth of Fourier coefficients of Siegel modular forms (Automorphic Representations and Related Topics)

Bocherer Siegfried , Das Soumya

RIMS Kokyuroku (1871), 136-144, 2013-12

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14

On the Fourier coefficients of Hilbert modular forms of half-integral weight over arbitrary algebraic number fields

Hisashi KOJIMA

Tsukuba Journal of Mathematics 37(1), 1-11, 2013-07

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15

The values of Hilbert-Eisenstein series at cusps

Shigeaki TSUYUMINE , 露峰茂明

… The Fourier coefficients, in particular the constant terms, of Hilbert-Eisenstein series have the number theoretic importance. … The value at a cusp gives the constant terms of the Fourier expansion centered at the cusp. …

三重大学教育学部研究紀要 64, 1-20, 2013

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16

On Fourier coefficients of some meromorphic modular forms

Honda Yutaro , Kaneko Masanobu , 本多雄太朗 , 金子昌信

… We prove a congruence modulo a prime of Fourier coefficients of several meromorphic modular forms of low weights. … We prove the result by establishing a generalization of a theorem of Garthwaite. …

Bulletin of the Korean Mathematical Society 49(6), 1349-1357, 2012-11

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17

A Note on Estimates of Fourier Coefficients of Weakly Holomorphic Modular Forms

HEIM Bernhard , MURASE Atsushi

… Here, we give a detailed account of a proof for the estimates of Fourier coefficients of weakly holomorphic modular forms, which play an important role in the study of Borcherds lifts. …

Acta humanistica et scientifica universitatis Sangio Kyotiensis. Natural science series -(41), 69-77, 2012-03

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18

ON THE FOURIER COEFFICIENTS OF JACOBI FORMS OF INDEX $N$ OVER TOTALLY REAL NUMBER FIELDS

KOJIMA HISASHI

… Skoruppa and Zagier established a bijective correspondence from the space of Jacobi forms $\phi$ of index $m$ to that of elliptic modular forms $f$ of level $m$. … Gross, Kohnen and Zagier formulated this correspondence by means of kernel functions. …

Tohoku Mathematical Journal, Second Series 64(3), 361-385, 2012

J-STAGE
19

ON FOURIER COEFFICIENTS OF SIEGEL MODULAR FORMS OF DEGREE TWO WITH RESPECT TO CONGRUENCE SUBGROUPS

CHIDA MASATAKA , KATSURADA HIDENORI , MATSUMOTO KOHJI

Hokkaido University Preprint Series in Mathematics (990), 1-16, 2011-12-08

IR DOI
20

Toy models for D. H. Lehmer's conjecture

BANNAI Eiichi , MIEZAKI Tsuyoshi

… In 1947, Lehmer conjectured that the Ramanujan τ-function τ(m) never vanishes for all positive integers m, where τ(m) are the Fourier coefficients of the cusp form Δ24 … of weight 12. …

Journal of the Mathematical Society of Japan 62(3), 687-705, 2010-07-01

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