Special values of twisted symmetric square -functions and the trace formula
Sur les séries associées aux formes modulaires
The binary Goldbach conjecture with primes in arithmetic progressions with large modulus
It is proved that for almost all prime numbers , any fixed integer b₂, (b₂,k) = 1, and almost all integers b₁, 1 ≤ b₁ ≤ k, (b₁,k) = 1, almost all integers n satisfying n ≡ b₁ + b₂ (mod k) can be written as the sum of two primes p₁ and p₂ satisfying , i = 1,2. For the proof of this result, new estimates for exponential sums over primes in arithmetic progressions are derived.
The distribution of the eigenvalues of Hecke operators
The first negative Hecke eigenvalue of a Siegel cusp form of genus two
The Trace of Hecke Operators.
Trace formulae and applications to class numbers
In this paper we compute the trace formula for Hecke operators acting on automorphic forms on the hyperbolic 3-space for the group PSL2() with being the ring of integers of an imaginary quadratic number field K of class number H K > 1. Furthermore, as a corollary we obtain an asymptotic result for class numbers of binary quadratic forms.
Über die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung
Über eine Spurbildung bei automorphen Formen.
Weight reduction for cohomological mod modular forms over imaginary quadratic fields
Let be an imaginary quadratic field and its ring of integers. Let be a non-zero ideal and let be a rational inert prime in and coprime with . Let be an irreducible finite dimensional representation of . We establish that a system of Hecke eigenvalues appearing in the cohomology with coefficients in already lives in the cohomology with coefficients in for some ; except possibly in some few cases.
Об одном совете Ю.В. Линника, операторах Гекке и тета-функциях