Multiple zeta values & modular forms Lecture 12: The formal double zeta space & Period polynomials, (Lecture notes v.3.10) 3rd July 2020

Recall Formal double zeta space

H

H

Oddweishth

evenweishtk

Today Proof ZKHEZK.kzKAKEKZeyer Kinodd4,23

neuen

rThe f invariant pairing GF Paz 64k nein pol degree K 244min21

the eF II Ted

anu

ÄEHEKT747

ETHIKb

ET 2 anti automorphism induced byg y

Feh gives relation

FI in LF Rn

GoalZum zu

mir even Want Zum ZK.intZKmn K KirkoddWant Fm nett with Tod It s

ZK

MiB

Finding Fun GenserieOfbernoullir V Polyn

fm.lv HtE sT

Recall Realizations for all K A IQ algebra

4 Lu 9k realizationofDninAAT HomalDk A

allzu Hu

Ya Realization of Din R

Yak KK KH

Realization of Din 0997HK GK KH

a Ein

p

Period polynomials fes flied

E EVk

EKKH

Pf E Wk

9 E Ü Heigenspaces of Ef Evt X FAXfer f x y f IX Y

f Voivod _eigenspaces of S

Lewisequation

f ESK Pf Pf Odd even

later PI Ihr Cl WIPeriod of 6K

Fact 7 basis of 5K seth image is in WI

4dPEYCQCG.Q.beev v

Thes pacePff KalPa QtDK

wies per

PEWi

PIT

MuP X Y KIKI 6K

Porn EklundKitKEKKinodd