Shtukas and the Taylor expansion of L-functions
نویسندگان
چکیده
منابع مشابه
Taylor Expansion for the Entropy Rate of Hidden Markov Chains
We study the entropy rate of a hidden Markov process, defined by observing the output of a symmetric channel whose input is a first order Markov process. Although this definition is very simple, obtaining the exact amount of entropy rate in calculation is an open problem. We introduce some probability matrices based on Markov chain's and channel's parameters. Then, we try to obtain an estimate ...
متن کاملTaylor Expansion of Logic Functions: From Conventional to Nanoscale Design
The paper revisits the well-known spectral transforms of a Boolean function, emphasizing on the fact that ReedMuller, arithmetic and Walsh spectra can be calculated through boolean difference, and arithmetical and Walsh analogs of it. This techniques is called Taylor technique, by analogy with Taylor series which coefficients are differences, or differentials. The algorithms are perfectly imple...
متن کاملexistence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types
بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی بیان شده اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...
15 صفحه اولShtukas for Reductive Groups and Langlands Correspondence for Functions Fields
This text gives an introduction to the Langlands correspondence for function fields and in particular to some recent works in this subject. We begin with a short historical account (all notions used below are recalled in the text). The Langlands correspondence [Lan70] is a conjecture of utmost importance, concerning global fields, i.e. number fields and function fields. Many excellent surveys a...
متن کاملThe Taylor expansion of Ruelle L-function at the origin and the Borel regulator
We will prove that Ruelle L-function for a cuspidal unitary local system on an odd dimensional complete hyperbolic manifold with finite volume satisfies a functional equation and an analogue of Riemann hypothesis. We will also compute its Laurent expansion at the origin and will prove that the second coefficient coincides with a rational multiple of the volume up to a certain contribution from ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2017
ISSN: 0003-486X
DOI: 10.4007/annals.2017.186.3.2