Sentence examples for modular functions of from inspiring English sources

In this book, Goro Shimura provides the most comprehensive generalizations of this type by stating several reciprocity laws in terms of abelian varieties, theta functions, and modular functions of several variables, including Siegel modular functions.

In all the known examples like in  [21,5,11 13] the spaces S i are defined to be subspaces of the space of modular functions on Γ 0 having integer coefficients in their q -expansions.

For ℓ = 5 the S i are subrings of the ring of modular functions on Γ 0 which are isomorphic to Z [ X ], and a close inspection of Watson's computations of the U (i ) -actions makes transparent that here one heavily exploits the simple structure of Z [ X ].

But additionally he defines spaces X (i ) ⊆ S i of modular functions on Γ 0 (11 ) having integer coefficients in their q -expansions.

This suggests to consider subspaces S i of the modular functions on Γ 0 (20 ).

These data confirm a modular function of CR1 in SWI/SNF recruitment and show the feasibility of proteomic expression screening approaches with transactivation modules that contain or lack post-translational modifications to uncover differential protein interactions.

Let K (N ) denote the set of all modular functions for Γ 0 (N ), i.e. K (N ) = M 0 !

In short, we were able to recover ℓ -adic zero convergence by the introduction of a new type of subspaces of modular functions which behave well under the action of the U -operators.

The proofs of all these identities and congruences heavily depend upon the theory of modular functions and the properties of Eisenstein series.

1998 Fields Medal winner Richard Borcherds succeeded to prove the monstrous moonshine conjectures, a surprising and deep relation of the largest finite simple sporadic group the "monster group"—with certain modular functions, a piece of classical complex analysis, and string theory, a theory supposed to unify the description of many physical phenomena.

The Moonshine conjectures asserted a mysterious connection between certain families of modular functions and the representation theory of the largest sporadic simple group (the "Monster").