Interaction sums and action of Hecke operators on theta-series
Anatoli Andrianov (2009)
Acta Arithmetica
E. GOTTSCHLING (1968/1969)
Inventiones mathematicae
Hidenori Katsurada, Hisa-aki Kawamura (2014)
Acta Arithmetica
Let k and n be positive even integers. For a cuspidal Hecke eigenform h in the Kohnen plus space of weight k - n/2 + 1/2 for Γ₀(4), let f be the corresponding primitive form of weight 2k-n for SL₂(ℤ) under the Shimura correspondence, and Iₙ(h) the Duke-Imamoḡlu-Ikeda lift of h to the space of cusp forms of weight k for Spₙ(ℤ). Moreover, let be the first Fourier-Jacobi coefficient of Iₙ(h), and be the cusp form in the generalized Kohnen plus space of weight k - 1/2 corresponding to under the...
Richard Taylor (1994)
Inventiones mathematicae
Michael Harris, D. Soudry, R. Taylor (1993)
Inventiones mathematicae
Riccardo Salvati Manni (1993)
Journal für die reine und angewandte Mathematik
Petra Ploch (1991)
Acta Arithmetica
Rainer Weissauer (1992)
Mathematische Zeitschrift
Alice Silverberg (1985)
Inventiones mathematicae
Soumya Das, Winfried Kohnen, Jyoti Sengupta (2012)
Acta Arithmetica
Toshiyuki Kikuta, Shoyu Nagaoka (2008)
Acta Arithmetica
Michio Ozeki (2011)
Acta Arithmetica
Rainer Weissauer (1992)
Compositio Mathematica
N.V. Proskurin (1988)
Journal für die reine und angewandte Mathematik
Siegfried Böcherer, Francesco Ludovico Chiera (2008)
Annales de l’institut Fourier
We prove that the Dirichlet series of Rankin–Selberg type associated with any pair of (not necessarily cuspidal) Siegel modular forms of degree and weight has meromorphic continuation to . Moreover, we show that the Petersson product of any pair of square–integrable modular forms of weight may be expressed in terms of the residue at of the associated Dirichlet series.
Shin-ichiro Mizumoto (1996)
Manuscripta mathematica
Anatoli Andrianov (2012)
Acta Arithmetica
Takashi Fukuda, Keiichi Komatsu (2003)
Journal de théorie des nombres de Bordeaux
Using the special values of Siegel modular functions, we construct Minkowski units for the ray class field of modulo . Our work is based on investigating the prime decomposition of the special values and describing explicitly the action of the Galois group for the special values. Futhermore we construct the full unit group of using modular and circular units under the GRH.
Toshiyuki Kikuta (2012)
Acta Arithmetica
Yoshinori Mizuno (2008)
Acta Arithmetica