In recent years a new science frontier emerged under the umbrella term of second-order science which creates new and challenging problems through a characteristic re-entry-operation like in pattern of patterns, learning of learning, cybernetics of cybernetics or logic of logic, which works with and on building blocks or elements of traditional or first-order scientific research and which, due t...

Wepresent a typing concept for second-order term graphsthat doesnot consider the types as an external add-on, but as an integral part of the term graph structure. This allows a homogeneous treatment of term-graph representationsof many kinds of typing systems, including second-order λ-calculi and systems of dependent types. Applications can be found in interactive systems and as typed intermedi...

The leading term of Eisenstein series and L-functions are well-known to be extremely important and to have very important arithmetic implications. For example, one may consider the analytic class number formula, The Siegel-Weil formula, the Birch and Swinnerton-Dyer conjecture, Stark’s conjectures, and Beilinson’s and Bloch-Kato conjectures. These are well-documented and are central in current ...