Sommaire du Fascicule no. 1

• $\ell$-torsion in class groups of certain families of $D_4$-quartic fields

  Chen An

  

  p. 1-23

• Reduction of certain crystalline representations and local constancy in the weight space

  Shalini Bhattacharya

  

  p. 25-47

• The endomorphism ring of projectives and the Bernstein centre

  Alexandre Pyvovarov

  

  p. 49-71

• Root number of twists of an elliptic curve

  Julie Desjardins

  

  p. 73-101

• The distribution of sums and products of additive functions

  Greg Martin ; Lee Troupe

  

  p. 103-131

• On the $p$-adic Langlands correspondence for algebraic tori

  Christopher Birkbeck

  

  p. 133-158

• Numerical verification of the Cohen–Lenstra–Martinet heuristics and of Greenberg’s $p$-rationality conjecture

  Razvan Barbulescu ; Jishnu Ray

  

  p. 159-177

• Linear relations with conjugates of a Salem number

  Artūras Dubickas ; Jonas Jankauskas

  

  p. 179-191

• On Tate’s conjecture for the elliptic modular surface of level $N$ over a prime field of characteristic $1\mathrm{mod}N$

  Rémi Lodh

  

  p. 193-204

• Ramanujan–Bernoulli numbers as moments of Racah polynomials

  Frédéric Chapoton

  

  p. 205-215

• Partial sums of the cotangent function

  Sandro Bettin ; Sary Drappeau

  

  p. 217-230

• Bounds of the rank of the Mordell–Weil group of Jacobians of Hyperelliptic Curves

  Harris B. Daniels ; Álvaro Lozano-Robledo ; Erik Wallace

  

  p. 231-258

• On finiteness of odd superperfect numbers

  Tomohiro Yamada

  

  p. 259-274

• A step beyond Freiman’s theorem for set addition modulo a prime

  Pablo Candela ; Oriol Serra ; Christoph Spiegel

  

  p. 275-289

• Fields of definition of rational curves of a given degree

  David Holmes ; Nick Rome

  

  p. 291-310