Comparison of Cusp Forms on $GL(3,{\bf Z})$

On the Coeecients of Cusp Forms

On the Existence and Temperedness of Cusp Forms for SL3(Z)

We develop a partial trace formula which circumvents some technical difficulties in computing the Selberg trace formula for the quotient SL3(Z)\SL3(R)/SO3(R). As applications, we establish the Weyl asymptotic law for the discrete Laplace spectrum and prove that almost all of its cusp forms are tempered at infinity. The technique shows there are non-lifted cusp forms on SL3(Z)\SL3(R)/SO3(R) as w...

Families of Cusp Forms

1. Families of cusp forms and the local equidistribution problem 2 2. Families of L-functions 6 3. Analogy with sieve 8 4. Examples of local equidistribution 8 5. Families of cusp forms according to Sarnak’s letter 11 6. Families of L-functions according to Conrey, Farmer, Keating, Rubinstein and Snaith 13 7. Direct consequences of strong local equidistribution 14 8. Quantitative local equidist...

Maaß Cusp Forms on SL(2,R)

The present text is course material for a minicourse on Maaß cusp forms I gave at Metz University in March 2005 as a part of the Sokrates partnership activities between the universities in Metz and Paderborn. This course may be viewed as the first joint activity in the context of the new International Research Training Group " Geometry and Analysis of Symmetries " (see http://irtg.upb.de) locat...

Primitive Cusp Forms

For example, let f11A denote the (unique) level 11 weight 2 cusp form, then both f11A(z) and f11A(2z) are level 22 cusp forms. Similarly, both f14A(z) and f14A(2z) are level 28 cusp forms, and both f15A(z) and f15A(2z) are level 30 cusp forms. None of these are “new” at N = 22, 28 or 30 since they arise from lower levels. Define S k (N) to be the vector space of weight k primitive cusp forms (o...