L-functions
Non vanishing of Artin twisted L functions of elliptic curves
... = L(π, s − ...automorphic L-functions in the literature: in particu- lar, in [10] Rohrlich shows the existence of infinitely many ray class characters χ such that L(π ⊗ χ, β) 6= 0 for any β ∈ ...
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Wach modules and critical slope p adic L functions
... p-adic L-function at- tached to an ordinary modular form using the methods of ...p-adic L-function, and we show that our results match the behaviour observed in examples calculated by Pollack and Stevens in ...
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The L functions and modular forms database project
... 2 L-functions arise as follows: they either are products of two degree 1 L-functions, or come from elliptic curves over Q, or from (a special kind of) modular ...same ...
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Mock period functions, sesquiharmonic Maass forms, and non critical values of L functions
... Non-critical values are much less understood and there are even some “negative” results such as that of Koblitz [26], asserting that, in a strong sense, there can not be a Period Theorem for non-critical values. In any ...
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A note on p adic Rankin Selberg L functions
... p-adic L-function, constructed using Beilinson– Flach elements, with two families of “analytic” p-adic ...2-variable functions, denoted here by superscripts ♠ and ♦, are defined over 2-variable slices of ...
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P adic L functions of Bianchi modular forms
... p-adic L-functions have been a subject of considerable ...p-adic L-functions control the size of cohomology groups of Galois ...p-adic L-function of a suitable rational modular ...
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Period polynomials, derivatives of L functions, and zeros of polynomials
... The period polynomial provides a way of encoding critical values of L-functions associated to modular cusp forms that has proven very successful in the uncovering of important arithmetic properties of ...
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An Integral Representation of Standard Automorphic L Functions for Unitary Groups
... [7] A. Borel, “Automorphic L-functions,” in Automorphic Forms, Representations and L-Functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977)—Part 2, vol. 33 of Proc. ...
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On mean values of mollifiers and L functions associated to primitive cusp forms
... 1.5. Proportions of zeros on the critical line. In this paper we revise the techniques of [7] for a mollifier consisting of several pieces. This approach is extremely general. As an application, we modestly increase the ...
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Iwasawa theory and p adic L functions over Zp2 extensions
... p-adic L-functions of an ordinary CM modular ...p-adic L-function, one arising from Kato’s Euler system and a second from p-adic modular ...Katz L-function for the CM ...the L-function ...
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Critical slope p adic L functions of CM modular forms
... p-adic L-functions are only defined up to multiplication by a nonzero constant for characters of each sign; in Kato’s construction these constants correspond to the choice of γ, whose projection to each of ...
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On Critical Values of L-Functions for Holomorphic Forms on GSp(4) X GL(2)
... We also note that the integral representation (Theorem 3.6.1) is of interest for several other applications. For instance, we hope that this integral representation will pave the way to certain new results involving ...
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On Mordell–Weil groups and congruences between derivatives of twisted Hasse–Weil L functions
... Hasse-Weil L-functions associated to twists of A, normalised by a product of explicit equivariant regulators and periods, and to explicit predictions concerning the Galois structure of Tate-Shafarevich ...
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Nonvanishing of L-Functions for GL(n)
... an L-function inside the critical strip can encode impor- tant arithmetic ...of L-functions at the center of the critical strip is especially important in this sense, as suggested by its ties with ...
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Kernels for products of L functions
... The above theorem gives the link between Fourier coefficients of double Eisenstein series and arbitrary values of L-functions. We hope that this interesting connection will help shed light on L ∗ (f, ...
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Unified representation of the family of L functions
... 8. Kim, T: A new approach to q-zeta function. Adv. Stud. Contemp. Math. 11, 157-162 (2005) 9. Kim, T: A new approach to p-adic q-L-function. Adv. Stud. Contemp. Math. 12, 61-72 (2006) 10. Kim, T: On p-adic ...
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P adic L functions for GL(2)
... of L-functions has proved extremely fruitful in number theory for almost two centuries, and there are a wealth of research papers relating their critical values to impor- tant arithmetic ...p-adic ...
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The effect of repeated differentiation on L-functions
... Hecke L-functions, since the functional equation, analogously to the Riemann Xi-function, can be written with a single Gamma ...of L-functions generally includes a product of disparate Gamma ...
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Shtuka cohomology and special values of Goss L-functions
... Given a scheme X and an endomorphism τ we define an abelian category of shtukas on (X, τ ), prove that it has enough injectives and define a shtuka cohomology functor as the right derive[r] ...
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On two variable p-adic L-functions
... 7 CHAPTER 3: COLEMAN POWER SERIES AND LOGARITHMIC DERIVATIVES 12 CHAPTER 4: ELLIPTIC UNITS 20 CHAPTER 5: LOGARITHMIC DERIVATIVES OF ELLIPTIC UNITS 28 CHAPTER 6: SOME BASIC RESULTS ON THE[r] ...
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