viii CONTENTS

Specialization of forms in the presence of characteristic 2: ﬁrst steps

M. Knebusch 219

Representation of integers by special positive deﬁnite integral quadratic forms

W. Kohnen 243

Hyper-isotropy of bilinear forms in characteristic 2

A. Laghribi and P. Mammone 249

A historical view of the Pythagoras numbers of ﬁelds

D.B. Leep 271

The extensions of R-places and application

M. Machura and K. Osiak 289

Essential dimension

A.S. Merkurjev 299

On the Pﬁster number of quadratic forms

R. Parimala, V. Suresh, and J.-P. Tignol 327

Martin Kneser’s work on quadratic forms and algebraic groups

R. Scharlau 339

Enumerating perfect forms

A. Schurmann

¨

359

Reduction mod of Theta Series of Level

n

N.-P. Skoruppa 379

On a reciprocity theorem of Gauss

L.H. Walling 391

A bound of the number of reduced Arakelov divisors of a number ﬁeld

T. Watanabe and R. Yoshimitsu 399