We devise a new criterion for linear independence over function fields. Using this tool in the setting of dual t-motives, we find that all algebraic relations among special values geometric field Gamma-function are explained by standard functional equations.

We investigate periods, quasi-periods, logarithms, and quasi-logarithms of Anderson <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="t"> <mml:semantics> <mml:mi>t</mml:mi> <mml:annotation encoding="application/x-tex">t</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-modules, as well their hyperderivatives. develop a comprehensive account how these values can be obtained through rigid analytic trivializations abelian...

Characteristic p multizeta values were initially studied by Thakur, who defined them as analogues of classical multiple zeta Euler. In the present paper we establish an effective criterion for Eulerian values, which characterizes when a value is rational power Carlitz period. The resulting " t -motivic" algorithm can tell us whether any given or not. We also prove that if \zeta_{A}(s_{1},\ldots,s_{r}) Eulerian, then \zeta_{A}(s_{2},\ldots,s_{r}) has to be Eulerian. This was conjectured Lara...

Gaussian hypergeometric functions and traces of Hecke operators Get access Sharon Frechette, Frechette Search for other works by this author on: Oxford Academic Google Scholar Ken Ono, Ono Matthew Papanikolas International Mathematics Research Notices, Volume 2004, Issue 60, Pages 3233–3262, https://doi.org/10.1155/S1073792804132522 Published: 01 January 2004 Article history Received: 21 August 2003 Revision received: 08 March Accepted: 23

Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="rho"> <mml:semantics> <mml:mi>ρ<!-- ρ --></mml:mi> <mml:annotation encoding="application/x-tex">\rho</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a Drinfeld alttext="upper A"> <mml:mi>A</mml:mi> encoding="application/x-tex">A</mml:annotation> </inline-formula>-module with generic characteristic defined over an algebraic function field. We prove that all of...

Although links between values of finite field hypergeometric functions and eigenvalues elliptic modular forms are well known, we establish in this paper that there also connections to Siegel higher degree. Specifically, relate the eigenvalue Hecke operator index p a eigenform degree 2 level 8 special value 4 F 3 -hypergeometric function.

For any rank $2$ Drinfeld module $\rho$ defined over an algebraic function field, we consider its period matrix $P_{\rho}$, which is analogous to the of elliptic curve a number field. Suppose that characteristic finite field ${\Bbb F}_q$ odd and does not have complex multiplication. We show transcendence degree generated by entries $P_{\rho}$ F}_q(\theta)$ $4$. As consequence, also independence logarithms functions are linearly independent F}_q(\theta)$.

We investigate the arithmetic nature of special values Thakur's function field Gamma at rational points.Our main result is that all linear dependence relations over algebraic functions are consequences Anderson-Deligne-Thakur bracket relations.

We determine formulas for Ramanujan’s <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="tau"> <mml:semantics> <mml:mi>τ</mml:mi> <mml:annotation encoding="application/x-tex">\tau</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-function and the coefficients of modular forms on alttext="normal upper Gamma 0 left-parenthesis 2 right-parenthesis"> <mml:mrow> <mml:msub> <mml:mi mathvariant="normal">Γ</mml:mi>...

Let rho be a Drinfeld A-module with generic characteristic defined over an algebraic function field. We prove that all of the relations among periods, quasi-periods, and logarithms points on are those coming from linear induced by endomorphisms rho.

We investigate the combinatorial properties of traces nth Hecke operators on spaces weight 2k cusp forms level N. establish examples in which these are expressed terms classical objects enumerative combinatorics (e.g., tilings and Motzkin paths). general that explicit rational linear combinations values Gegenbauer (also known as ultraspherical) polynomials. These results arise from "packaging" into power series aspect. generating functions easily computed by using Eichler-Selberg trace formula.