ON PERIODS OF CUSP FORMS

COMPARISON RESULTS FOR CERTAIN PERIODS OF CUSP FORMS ON GL2n OVER A TOTALLY REAL NUMBER FIELD

This article grew out of my talk in ‘The Legacy of Srinivasa Ramanujan’ conference where I spoke about some techniques to prove algebraicity results for the special values of symmetric cube L-functions attached to the Ramanujan ∆-function. If one wishes to compare these different techniques, then one needs to compare various automorphic periods attached to the symmetric cube transfer of ∆. Moti...

On the Coeecients of Cusp Forms

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...

Periods of Cusp Forms and Elliptic Curves over Imaginary Quadratic Fields

In this paper we explore the arithmetic correspondence between, on the one hand, (isogeny classes of) elliptic curves E defined over an imaginary quadratic field K of class number one, and on the other hand, rational newforms F of weight two for the congruence subgroups r0(n), where n is an ideal in the ring of integers R of K . This continues work of the first author and forms part of the Ph.D...