81 citations · 318 across the 48 of their papers we have counts for
7 papers · 1 filter
Homotopy Spectra and Diophantine Equations
Yuri I. Manin, Matilde Marcolli
Arguably, the first bridge between vast, ancient, but disjoint domains of mathematical knowledge, - topology and number theory, - was built only during the last fifty years. This b…
Modular forms of real weights and generalized Dedekind symbols
Yuri I. Manin
In a previous paper, I have defined non--commutative generalized Dedekind symbols for classical --cusp forms using iterated period polynomials. Here I generalize this con…
Numbers as functions
Yuri I. Manin
In this survey I discuss A. Buium's theory of ``differential equations in the p-adic direction'' ([Bu05]) and its interrelations with ``geometry over fields with one element'', on…
Non-commutative generalized Dedekind symbols
Yuri I. Manin
We define and study generalized Dedekind symbols with values in non--necessarily commutative groups, generalizing constructions of Sh. Fukuhara in [Fu1], [Fu2]. Basic examples of s…
Remarks on modular symbols for Maass wave forms
Yu I. Manin
In this paper I introduce modular symbols for Maass wave cusp forms. They appear in the guise of finitely additive functions on the Boolean algebra generated by intervals with non-…
Modular shadows and the Levy-Mellin infinity-adic transform
Yuri Manin, Matilde Marcolli
This paper continues the study of the structures induced on the ``invisible boundary'' of the modular tower and extends some results of math.NT/0102006. We start with a systematic…
Iterated integrals of modular forms and noncommutative modular symbols
Yu. I. Manin
The main goal of this paper is to study properties of the iterated integrals of modular forms in the upper halfplane, eventually multiplied by , along geodesics connecting…