Nonstandard Mathematics and New Zeta and L-Functions

Abstract

This Ph.D. thesis, prepared under the supervision of Professor Ivan Fesenko, defines new zeta functions in a nonstandard setting and their analytical properties are developed. Further, p-adic interpolation is presented within a nonstandard setting which enables the concept of interpolating with respect to two, or more, distinct primes to be defined. The final part of the dissertation examines the work of M. J. Shai Haran and makes initial attempts of viewing it from a nonstandard perspective.

Ph.D. Thesis, University of Nottingham, 2007, 163 pages

References in corpus (9)

• New Approach to Arakelov Geometry
• Sums of powers of consecutive q-integers
• A note on q-Volkenborn integration
• On the twisted $q$-zeta functions and $q$-Bernoulli polynomials
• q-Analogues of the Riemann zeta, the Dirichlet L-functions, and a crystal zeta function
• Integral representations of q-analogues of the Hurwitz zeta function
• A note on q-Bernoulli numbers and polynomials
• Nonstandard Etale Cohomology
• On the q-analogue of two-variable p-adic L-function