Results 281 to 290 of about 95,973 (316)

Maximum entropy networks show that plant-arbuscular mycorrhizal fungal associations are anti-nested and modular

Ajaz S, Amin N, López-García Á, Birt H, Pajares-Murgó M, Lanfranco L, Garrido JL, Alcántara JM, Rillig MC, Johnson D, Caruso T.   +10 more
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 -INVARIANT AND MODULAR FORMS [PDF]

The Quarterly Journal of Mathematics, 2014
We show that the Atiyah-Patodi-Singer reduced $ $-invariant of the twisted Dirac operator on a closed $4m-1$ dimensional spin manifold, with the twisted bundle being the Witten bundle appearing in the theory of elliptic genus, is a meromorphic modular form of weight $2m$ up to an integral $q$-series.
Fei Han, Weiping Zhang
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Modular Forms

2008
Modular forms are functions with an enormous amount of symmetry that play a central role in number theory, connecting it with analysis and geometry. They have played a prominent role in mathematics since the 19th century and their study continues to flourish today.
Edixhoven, B., van der Geer, G., Moonen, B.   +2 more
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Modular Forms

Oberwolfach Reports, 2015
The theory of Modular Forms has been central in mathematics with a rich history and connections to many other areas of mathematics. The workshop explored recent developments and future directions with a particular focus on connections to the theory of periods.
Jan Hendrik Bruinier, Atsushi Ichino, Tamotsu Ikeda, Özlem Imamoglu   +3 more
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Modular Forms on Schiermonnikoog

2008
Modular forms are functions with an enormous amount of symmetry that play a central role in number theory, connecting it with analysis and geometry. They have played a prominent role in mathematics since the 19th century and their study continues to flourish today.
Edixhoven, B., van der Geer, G., Moonen, B.   +2 more
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The Values of Modular Functions and Modular Forms

Canadian Mathematical Bulletin, 2006
AbstractLet Γ0be a Fuchsian group of the first kind of genus zero and Γ be a subgroup of Γ0of finite index of genus zero. We find universal recursive relations giving theqr-series coefficients ofj0by using those of theqhs-series ofj, wherejis the canonical Hauptmodul for Γ andj0is a Hauptmodul for Γ0without zeros on the complex upper half plane(hereqℓ:=
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Modular Groups and Modular Forms

1989
In this chapter, we explain the general theory of modular forms. In §4.1, we discuss the full modular group SL 2(ℤ) and modular forms with respect to SL 2(ℤ), as an introduction to the succeeding sections. We define and study congruence modular groups in §4.2. In §4.3, we explain the relation between modular forms and Dirichlet series obtained by Hecke
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