Differential Operators and Theta Series
نویسندگان
چکیده
منابع مشابه
Differential Operators and the Wheels Power Series
An earlier work of the author’s showed that it was possible to adapt the Alekseev-Meinrenken Chern-Weil proof of the Duflo isomorphism to obtain a completely combinatorial proof of the Wheeling isomorphism. That work depended on a certain combinatorial identity, which said that a certain composition of elementary combinatorial operations arising from the proof was precisely the Wheeling operati...
متن کاملAction of Hecke Operators on Siegel Theta Series Ii
We apply the Hecke operators T (p) and T ′ j (p) (1 ≤ j ≤ n ≤ 2k) to a degree n theta series attached to a rank 2k Z-lattice L equipped with a positive definite quadratic form in the case that L/pL is regular. We explicitly realize the image of the theta series under these Hecke operators as a sum of theta series attached to certain sublattices of 1 p L, thereby generalizing the Eichler Commuta...
متن کاملAction of Hecke Operators on Siegel Theta Series I
We apply the Hecke operators T (p) and T̃j(p 2) (1 ≤ j ≤ n, p prime) to a degree n theta series attached to a rank 2k Z-lattice L, n ≤ k, equipped with a positive definite quadratic form in the case that L/pL is hyperbolic. We show that the image of the theta series under these Hecke operators can be realized as a sum of theta series attached to certain closely related lattices, thereby generali...
متن کاملGenus Theta Series, Hecke Operators and the Basis Problem for Eisenstein Series
We derive explicit formulas for the action of the Hecke operator T (p) on the genus theta series of a positive definite integral quadratic form and prove a theorem on the generation of spaces of Eisenstein series by genus theta series. We also discuss connections of our results with Kudla’s matching principle for theta integrals.
متن کاملMicrosolutions of differential operators and values of arithmetic Gevrey series
We continue our investigation of E-operators, in particular their connection with G-operators; these differential operators are fundamental in understanding the diophantine properties of Siegel’s E and G-functions. We study in detail microsolutions (in Kashiwara’s sense) of Fuchsian differential operators, and apply this to the construction of basis of solutions at 0 and∞ of any E-operator from...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1985
ISSN: 0002-9947
DOI: 10.2307/1999662