By Siegfried Bocherer, Tomoyoshi Ibukiyama, Masanobu Kaneko, Fumihiro Sato
"This quantity encompasses a number of articles provided at a convention on Automorphic types and Zeta features in reminiscence of Tsuneo Arakawa, an eminent researcher in modular varieties in different variables and zeta capabilities. The publication starts off with a evaluate of his works, through sixteen articles by way of specialists within the fields. This choice of papers illustrates Arakawa's contributions and the present tendencies in modular varieties in different variables and comparable zeta capabilities.
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Additional info for Automorphic Forms and Zeta Functions: Proceedings of the Conference in Memory of Tsuneo Arakawa Rikkyo University
38 R. 2. We can only hope that someone will come up with a prescription leading exactly to the formula fi(k' -k) = (1/2)(1 + (k' -k) + (cos(n(k' - k)/2))2). 5. +r'R. 1. We have for U* = k(Y* — Zt) + mR* Bv, (X, Y) = 2k (x (y' + z') - x' (y + z)) + 2m (pq' The associated symplectic form won M := M£m U(XM,YM) = -p'q). is defined by Bu,(X,Y). As usual, XM and YM denote the vector fields associated to X and Y : If h = h(xr,yt,pr,qt) is a function on M expressed in the parameters x*,y*,p*,q*, s. t. 2.
It turns out that in this case (say for newforms of haupttypus) the contribution from the ramified primes is a rational function with denominator independent of the cusp in question; the numerator has a simple structure (for nebentypus the situation is somewhat more complicated). It is this numerator, which - in some cases - may create an obstruction against a positive solution of the basis problem. Of course there is also a "global obstruction" coming from zeroes or poles of L-functions (in the case of low weights).
I := y> — 2
Automorphic Forms and Zeta Functions: Proceedings of the Conference in Memory of Tsuneo Arakawa Rikkyo University by Siegfried Bocherer, Tomoyoshi Ibukiyama, Masanobu Kaneko, Fumihiro Sato