Speeding up Subquadratic Finite Field Multiplier over GF(2m) Generated by Trinomials Using Toeplitz Matrix-Vector with Inner Product Formula

2011 ◽  
Author(s):  
Chiou-Yng Lee ◽  
Pramod Kumar Meher
Keyword(s):  
Finite Field ◽  
Toeplitz Matrix ◽  
Product Formula ◽  
Inner Product ◽  
Finite Field Multiplier ◽  
Matrix Vector

Polynomial identities between Hecke eigenforms

2019 ◽  
Vol 15 (10) ◽  
pp. 2135-2150
Author(s):  
Dianbin Bao
Keyword(s):  
Eisenstein Series ◽  
Product Formula ◽  
Inner Product ◽  
Polynomial Identities ◽  
Number Of Solutions ◽  
Hecke Eigenforms

In this paper, we study solutions to [Formula: see text], where [Formula: see text] are Hecke newforms with respect to [Formula: see text] of weight [Formula: see text] and [Formula: see text]. We show that the number of solutions is finite for all [Formula: see text]. Assuming Maeda’s conjecture, we prove that the Petersson inner product [Formula: see text] is nonzero, where [Formula: see text] and [Formula: see text] are any nonzero cusp eigenforms for [Formula: see text] of weight [Formula: see text] and [Formula: see text], respectively. As a corollary, we obtain that, assuming Maeda’s conjecture, identities between cusp eigenforms for [Formula: see text] of the form [Formula: see text] all are forced by dimension considerations. We also give a proof using polynomial identities between eigenforms that the [Formula: see text]-function is algebraic on zeros of Eisenstein series of weight [Formula: see text].

scholarly journals Product formula for p -adic epsilon factors

2014 ◽  
Vol 14 (2) ◽  
pp. 275-377 ◽  
Author(s):  
Tomoyuki Abe ◽  
Adriano Marmora
Keyword(s):  
Finite Field ◽  
Stationary Phase ◽  
Product Formula ◽  
Formula One ◽  
Etale Cohomology ◽  
Rigid Cohomology ◽  
Étale Cohomology ◽  
Analogous Formula ◽  
Epsilon Factors

AbstractLet $X$ be a smooth proper curve over a finite field of characteristic $p$. We prove a product formula for $p$-adic epsilon factors of arithmetic $\mathscr{D}$-modules on $X$. In particular we deduce the analogous formula for overconvergent $F$-isocrystals, which was conjectured previously. The $p$-adic product formula is a counterpart in rigid cohomology of the Deligne–Laumon formula for epsilon factors in $\ell$-adic étale cohomology (for $\ell \neq p$). One of the main tools in the proof of this $p$-adic formula is a theorem of regular stationary phase for arithmetic $\mathscr{D}$-modules that we prove by microlocal techniques.

Sign in / Sign up

Export Citation Format

Share Document