282 research outputs found
A strengthening of the GL(2) converse theorem
No full textWe generalize the method of A. R. Booker (Poles of Artin L-functions and the strong Artin conjecture, Ann. of Math. (2) 158 (2003), 1089–1098; MR 2031863(2004k:11082)) to prove a version of the converse theorem of Jacquet and Langlands with relaxed conditions on the twists by ramified idèle class characters.We generalize the method of A. R. Booker (Poles of Artin L-functions and the strong Artin conjecture, Ann. of Math. (2) 158 (2003), 1089–1098; MR 2031863(2004k:11082)) to prove a version of the converse theorem of Jacquet and Langlands with relaxed conditions on the twists by ramified idèle class characters
Weil's converse theorem with poles
No full textWe prove a generalization of the classical converse theorem of Weil, allowing the twists by non-trivial Dirichlet characters to have arbitrary poles.We prove a generalization of the classical converse theorem of Weil, allowing the twists by non-trivial Dirichlet characters to have arbitrary poles
Dr. Carroll Green (l), Ruth Waddy (c) and Claude Booker (r)
No full textDr. Carroll Green, art historian, Ruth Waddy, artist/author, and Claude Booker, President of the Black Arts Council at a conference at the Arena: 109 East Magnolia Stree
Bounds and algorithms for the K-Bessel function of imaginary order
No full textUsing the paths of steepest descent, we prove precise bounds with numerical implied constants for the modified Bessel function of imaginary order and its first two derivatives with respect to the order. We also prove precise asymptotic bounds on more general (mixed) derivatives without working out numerical implied constants. Moreover, we present an absolutely and rapidly convergent series for the computation of and its derivatives, as well as a formula based on Fourier interpolation for computing with many values of . Finally, we have implemented a subset of these features in a software library for fast and rigorous computation of
Further refinements of the GL(2) converse theorem
No full textWe improve the results of Booker and Krishnamurthy (Compos. Math. 147 (2011) 669–715) by allowing restricted sets of poles among the unramified twists. This allows for a clean statement of the GL(2) converse theorem which includes all cases of Eisenstein series
A conjectural extension of Hecke’s converse theorem
No full textWe formulate a precise conjecture that, if true, extends the converse theorem of Hecke without requiring hypotheses on twists by Dirichlet characters or an Euler product. The main idea is to linearize the Euler product, replacing it by twists by Ramanujan sums. We provide evidence for the conjecture, including proofs of some special cases and under various additional hypotheses.</p
Square-free values of reducible polynomials
No full textWe calculate admissible values of r such that a square-free polynomial with integer coefficients, no fixed prime divisor and irreducible factors of degree at most 3 takes infinitely many values that are a product of at most r distinct primes
Five Medieval Plays Production Photo
No full textProvidence College Department of Theatre, Dance & Film
Five Medieval Plays
1974
Director, R.L. Pelkington, O.P.
Music Director, Reginal Haller, O.P.
Instrumental Music, Gail Himrod, O.P.
Choreographer, L. R. Slavin
The Creation Cast: God - Nicolas Walker, Lucifer - John O\u27Hurley, Bad Angel - Nina Cowell, Good Angel - Lynn Cheney, Adam - Kevin Fortin, Eve - Tracy Quirk
The Annunciation/Salutation Cast: God - Robert Perry, Gabriel - Andrew Bourgeois, Joseph - Peter Thomson, Mary - Christine Mahoney, Elizabeth - Candice Cummings
The Second Shepard Cast: 1st Shepard - Arthur Williams, 2nd Shepard - Robert Perry, Angel - Mary Jane Booker, Max - James Belkin, Gill - Alex Tavares, The Lamb - Mary G. Deleppo
The Resurrection Cast: Pilate - John O\u27Hurley, Caiaphas - Robert Perry, Annas - Nicholas Walker, Centurion - James Belkin, Jesus - Peter Thomson, First Angel - Lynn Cheney, Second Angel - Nina Cowell, First Soldier - Andrew Bourgeois, Second Soldier - Kevin Fortin, Third Soldier - Arthur Williams, Mary Magdalene - Christine Mahoney, Mary Salome - Amy Carrion, Mary Jacobi - Mary Jane Booker
Photography by Thomas F. Maguire, Jr.https://digitalcommons.providence.edu/medievalplays_photos/1023/thumbnail.jp
L-functions as distributions
No full textWe define an axiomatic class of L-functions extending the Selberg class. We show in particular that one can recast the traditional conditions of an Euler product, analytic continuation and functional equation in terms of distributional identities akin to Weil’s explicit formula. The generality of our approach enables some new applications; for instance, we show that the L-function of any cuspidal automorphic representation of GL3(AQ) has infinitely many zeros of odd order
Finite connected components of the aliquot graph
No full textConditional on a strong form of the Goldbach conjecture, we determine all finite connected components of the aliquot graph containing a number less than 109, as well as those containing an amicable pair below 1014 or one of the known perfect or sociable cycles below 1017. Along the way we develop a fast algorithm for computing the inverse image of an even number under the sum-of-proper-divisors function.</p
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