Results 21 to 30 of about 158 (51)
, 2009 In analogy with the Riemann zeta function at positive integers, for each finite field F_p^r with fixed characteristic p we consider Carlitz zeta values zeta_r(n) at positive integers n. Our theorem asserts that among the zeta values in {zeta_r(1), zeta_r(
Chieh-Yu Chang +4 more
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Explicit L-functions and a Brauer-Siegel theorem for Hessian elliptic curves [PDF]
, 2017 For a finite field $\mathbb{F}_q$ of characteristic $p\geq 5$ and $K=\mathbb{F}_q(t)$, we consider the family of elliptic curves $E_d$ over $K$ given by $y^2+xy - t^dy=x^3$ for all integers $d$ coprime to $q$. We provide an explicit expression for the $L$
Griffon, Richard
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Smooth hypersurface sections containing a given subscheme over a finite field
, 2008 We use the "closed point sieve" to prove a variant of a Bertini theorem over finite fields. Specifically, given a smooth quasi-projective subscheme X of P^n of dimension m over F_q, and a closed subscheme Z in P^n such that Z intersect X is smooth of ...
Poonen, Bjorn
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Explicit Formulae for $L$-values in Positive Characteristic [PDF]
, 2014 We focus on the generating series for the rational special values of Pellarin's $L$-series in $1 \leq s \leq 2(q-1)$ indeterminates, and using interpolation polynomials we prove a closed form formula relating this generating series to the Carlitz ...
Perkins, Rudolph Bronson
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Newton Polygons of Cyclic Covers of the Projective Line Branched at Three Points [PDF]
, 2019 We review the Shimura–Taniyama method for computing the Newton polygon of an abelian variety with complex multiplication. We apply this method to cyclic covers of the projective line branched at three points.
Li, Wanlin +3 more
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A Generic Approach to Searching for Jacobians
, 2007 We consider the problem of finding cryptographically suitable Jacobians. By applying a probabilistic generic algorithm to compute the zeta functions of low genus curves drawn from an arbitrary family, we can search for Jacobians containing a large ...
Sutherland, Andrew V.
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Hypergeometric L-functions in average polynomial time
, 2020 We describe an algorithm for computing, for all primes $p \leq X$, the mod-$p$ reduction of the trace of Frobenius at $p$ of a fixed hypergeometric motive in time quasilinear in $X$.
Costa, Edgar +2 more
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Linear relations among double zeta values in positive characteristic
, 2016 The study of this paper is inspired by the conjecture of Zagier on the explicit dimension formula for the space of the same weight double zeta values in terms of the dimension of cusp forms for SL_{2}(Z).
Chang, Chieh-Yu
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Generic Newton polygons for curves of given p-rank [PDF]
, 2013 We survey results and open questions about the $p$-ranks and Newton polygons of Jacobians of curves in positive characteristic $p$. We prove some geometric results about the $p$-rank stratification of the moduli space of (hyperelliptic) curves.
Achter, Jeff, Pries, Rachel
core
On the Mordell-Weil lattice of y 2 = x 3 + b x + t 3 n + 1 in characteristic 3. [PDF]
Res Number Theory, 2022 Leterrier G.
europepmc +1 more source