Modular forms and $p$-adic numbers (in Russian)

Alexei Panchishkin

Modular forms and $p$-adic numbers (in Russian)

Number Theory 2007-09-12 v1

Authors: Alexei Panchishkin

Abstract

Let $p$ be a prime. We discuss $p$ -adic properties of various arithmetical functions related to the coefficients of modular form and generating functions. Modular forms are considered as a tool of solving arithmetical problems. Examples of congruences between modular forms modulo $p$ and modulo $p^n$ are given, and the use of a computer for the study of modular forms is illistrated.

Keywords

p-adic analysis modular forms prime number theory

Cite

@article{arxiv.0709.1611,
  title  = {Modular forms and $p$-adic numbers (in Russian)},
  author = {Alexei Panchishkin},
  journal= {arXiv preprint arXiv:0709.1611},
  year   = {2007}
}

Comments

in Russian, 2 figures

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