Computer assisted number theory with applications -- Successive diagonal projections of Hilbert modular functions -- Problems and results on minimal bases in additive number theory -- On the number of false witnesses for a composite number -- Arithmetic theory of Siegel modular forms -- What is the structure of K if K+K is small? -- The geometry of Markoff forms -- On the maximum of an exponential sum of the Möbius function -- Galois coverings of the arithmetic line -- Notes on elliptic K3 surfaces -- Splitting fields of principal homogeneous spaces -- Mechanics on a surface of constant negative curvature -- The depth of rings of invariants over finite fields -- On the congruence of modular forms -- Methods of factoring large integers -- Divisors of the Siegel modular variety.

This is the third Lecture Notes volume to be produced in the framework of the New York Number Theory Seminar. The papers contained here are mainly research papers. N.