Search
Search Results
-
Modular forms and an explicit Chebotarev variant of the Brun–Titchmarsh theorem
We prove an explicit Chebotarev variant of the Brun–Titchmarsh theorem. This leads to explicit versions of the best known unconditional upper bounds...
-
Public Key Cryptography
As we have seen, a cryptosystem is a system of the form...
-
Kuga Fiber Spaces
This chapter is in a sense the culmination of the various topics discussed in previous chapters; it arises by the restriction of the considered...
-
Asymptotics of Nahm sums at roots of unity
We give a formula for the radial asymptotics to all orders of the special q -hypergeometric series known as Nahm sums at complex roots of unity. This...
-
Background and Fundamental Concepts
This book is about doing computations with functions. Given a function, we may for example want to prove certain conjectures about it, to discover...
-
Locally Mixed Symmetric Spaces
This chapter introduces the notion which is the main interest in this book and is responsible for the title. Locally mixed symmetric spaces are a...
-
A note on additively completely regular seminearrings
In the endeavour of obtaining semigroup theoretic analogues i.e., the analogues of structure theorems of completely regular semigroups in the setting...
-
Invariants for trees of non-archimedean polynomials and skeleta of superelliptic curves
In this paper we generalize the j -invariant criterion for the semistable reduction type of an elliptic curve to superelliptic curves X given by
... 
-
Finite Quotients, Arithmetic Invariants, and Hyperbolic Volume
For any pair of orientable closed hyperbolic 3-manifolds, this paper shows that any isomorphism between the profinite completions of their...
-
Exponential Sums over Finite Fields
This is an expository paper on algebraic aspects of exponential sums over finite fields. This is a new direction. Various examples, results and open...
-
-
Near-Fields
This chapter concerns near-fields, particularly finite near-fields. It offers the most complete account of finite near-fields in English and contains...
-
A Local Analogue of the Ghost Conjecture of Bergdall–Pollack
We formulate a local analogue of the ghost conjecture of Bergdall and Pollack, which essentially relies purely on the representation theory of
... 
-
-
Appendices
In the appendix, notations used throughout the book are introduced, and a few topics are sketched; in addition the section references provides a...
-
Transgressions of the Euler class and Eisenstein cohomology of GLN(Z)
These notes were written to be distributed to the audience of the first author’s Takagi Lectures delivered June 23, 2018. These are based on a...
-
Semi-Analytical ERKN Integrators for Solving High-Dimensional Nonlinear Wave Equations
Incorporating the operator-variation-of-constants formula for high-dimensional nonlinear wave equations with Fast Fourier Transform techniques in...
-
Difference of a Hauptmodul for Γ0(N) and certain Gross-Zagier type CM value formulas
In this work, we show that the difference of a Hauptmodul for a genus zero group Γ 0 ( N ) as a modular function on Y 0 ( N ) × Y 0 ( N ) is a Borcherds lift of...